LMFDB - Embedded newform 37.10.c.a.10.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(10,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$27$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.15
Character	$\chi$	$=$	37.10
Dual form			37.10.c.a.26.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.41387 - 5.91300i) q^{2} +(41.2346 + 71.4204i) q^{3} +(232.691 + 403.033i) q^{4} +(-741.590 - 1284.47i) q^{5} +563.079 q^{6} +(721.322 + 1249.37i) q^{7} +6673.32 q^{8} +(6440.92 - 11156.0i) q^{9} +O(q^{10})$	\(q+(3.41387 - 5.91300i) q^{2} +(41.2346 + 71.4204i) q^{3} +(232.691 + 403.033i) q^{4} +(-741.590 - 1284.47i) q^{5} +563.079 q^{6} +(721.322 + 1249.37i) q^{7} +6673.32 q^{8} +(6440.92 - 11156.0i) q^{9} -10126.8 q^{10} +64912.9 q^{11} +(-19189.8 + 33237.8i) q^{12} +(1601.42 + 2773.74i) q^{13} +9850.01 q^{14} +(61158.4 - 105929. i) q^{15} +(-96355.9 + 166893. i) q^{16} +(-313509. + 543013. i) q^{17} +(-43976.9 - 76170.3i) q^{18} +(274128. + 474804. i) q^{19} +(345123. - 597770. i) q^{20} +(-59486.8 + 103034. i) q^{21} +(221605. - 383830. i) q^{22} +2.52992e6 q^{23} +(275171. + 476611. i) q^{24} +(-123350. + 213649. i) q^{25} +21868.1 q^{26} +2.68560e6 q^{27} +(-335690. + 581432. i) q^{28} +895575. q^{29} +(-417574. - 723259. i) q^{30} -615101. q^{31} +(2.36626e6 + 4.09849e6i) q^{32} +(2.67666e6 + 4.63611e6i) q^{33} +(2.14056e6 + 3.70755e6i) q^{34} +(1.06985e6 - 1.85304e6i) q^{35} +5.99497e6 q^{36} +(-8.70955e6 - 7.35564e6i) q^{37} +3.74335e6 q^{38} +(-132068. + 228748. i) q^{39} +(-4.94887e6 - 8.57169e6i) q^{40} +(7.10564e6 + 1.23073e7i) q^{41} +(406161. + 703492. i) q^{42} +2.99073e7 q^{43} +(1.51047e7 + 2.61620e7i) q^{44} -1.91061e7 q^{45} +(8.63684e6 - 1.49594e7i) q^{46} -6.46096e7 q^{47} -1.58928e7 q^{48} +(1.91362e7 - 3.31449e7i) q^{49} +(842204. + 1.45874e6i) q^{50} -5.17096e7 q^{51} +(-745271. + 1.29085e6i) q^{52} +(-3.39248e7 + 5.87594e7i) q^{53} +(9.16828e6 - 1.58799e7i) q^{54} +(-4.81388e7 - 8.33789e7i) q^{55} +(4.81361e6 + 8.33741e6i) q^{56} +(-2.26071e7 + 3.91567e7i) q^{57} +(3.05738e6 - 5.29554e6i) q^{58} +(7.11183e7 - 1.23180e8i) q^{59} +5.69240e7 q^{60} +(-2.56718e7 - 4.44648e7i) q^{61} +(-2.09988e6 + 3.63709e6i) q^{62} +1.85839e7 q^{63} -6.63560e7 q^{64} +(2.37519e6 - 4.11395e6i) q^{65} +3.65511e7 q^{66} +(-1.40571e8 - 2.43477e8i) q^{67} -2.91803e8 q^{68} +(1.04320e8 + 1.80688e8i) q^{69} +(-7.30467e6 - 1.26521e7i) q^{70} +(1.59188e8 + 2.75722e8i) q^{71} +(4.29823e7 - 7.44475e7i) q^{72} -4.42164e7 q^{73} +(-7.32272e7 + 2.63884e7i) q^{74} -2.03452e7 q^{75} +(-1.27574e8 + 2.20965e8i) q^{76} +(4.68231e7 + 8.11000e7i) q^{77} +(901724. + 1.56183e6i) q^{78} +(9.30295e6 + 1.61132e7i) q^{79} +2.85826e8 q^{80} +(-1.60371e7 - 2.77770e7i) q^{81} +9.70310e7 q^{82} +(9.26657e6 - 1.60502e7i) q^{83} -5.53682e7 q^{84} +9.29980e8 q^{85} +(1.02100e8 - 1.76842e8i) q^{86} +(3.69287e7 + 6.39623e7i) q^{87} +4.33185e8 q^{88} +(1.56999e8 - 2.71930e8i) q^{89} +(-6.52257e7 + 1.12974e8i) q^{90} +(-2.31027e6 + 4.00151e6i) q^{91} +(5.88690e8 + 1.01964e9i) q^{92} +(-2.53634e7 - 4.39308e7i) q^{93} +(-2.20569e8 + 3.82037e8i) q^{94} +(4.06582e8 - 7.04220e8i) q^{95} +(-1.95144e8 + 3.37999e8i) q^{96} -6.21385e8 q^{97} +(-1.30657e8 - 2.26305e8i) q^{98} +(4.18099e8 - 7.24168e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) $ 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9 - 82404 * q^10 - 108196 * q^11 + 45492 * q^12 - 29827 * q^13 - 504992 * q^14 + 87135 * q^15 - 1561814 * q^16 + 116991 * q^17 + 1767678 * q^18 - 599677 * q^19 + 4122556 * q^20 - 221017 * q^21 - 257914 * q^22 + 1752736 * q^23 + 1149408 * q^24 - 6037260 * q^25 - 16731604 * q^26 - 1916582 * q^27 + 1917318 * q^28 - 11336100 * q^29 - 20390006 * q^30 + 14447580 * q^31 - 873740 * q^32 - 4494200 * q^33 + 13736524 * q^34 - 8546699 * q^35 + 61692836 * q^36 - 1919410 * q^37 - 85447920 * q^38 - 14035313 * q^39 + 3210182 * q^40 + 28676571 * q^41 - 101904850 * q^42 + 56602028 * q^43 + 153011074 * q^44 + 104234980 * q^45 + 99535572 * q^46 - 147509100 * q^47 - 203670880 * q^48 - 201857540 * q^49 - 91421384 * q^50 + 328228338 * q^51 - 69374156 * q^52 + 59137361 * q^53 + 201615042 * q^54 - 219079762 * q^55 + 202573590 * q^56 - 5989161 * q^57 - 157098688 * q^58 + 137993791 * q^59 + 413427232 * q^60 - 244884419 * q^61 + 109345558 * q^62 - 995908592 * q^63 + 184008092 * q^64 + 248745395 * q^65 + 1965122248 * q^66 - 130143913 * q^67 + 667610796 * q^68 + 246927272 * q^69 - 291173360 * q^70 + 473387559 * q^71 + 366188748 * q^72 + 923638972 * q^73 - 885443390 * q^74 - 2185997392 * q^75 - 337459826 * q^76 - 586609928 * q^77 - 261025842 * q^78 + 563110723 * q^79 - 4210381784 * q^80 + 713813329 * q^81 + 3458576264 * q^82 - 663594441 * q^83 - 2635249016 * q^84 - 1417287750 * q^85 - 2269028474 * q^86 + 314944482 * q^87 - 7714172 * q^88 + 655027619 * q^89 + 588021376 * q^90 - 1833870961 * q^91 - 2384055268 * q^92 - 90092600 * q^93 - 1449940302 * q^94 + 2787158841 * q^95 + 2383567424 * q^96 - 2751583248 * q^97 + 4970876154 * q^98 + 2668760954 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.41387	−	5.91300i	0.150873	−	0.261320i	−0.780675	−	0.624937i	$-0.785125\pi$
$2$	3.41387	−	5.91300i	0.150873	−	0.261320i	0.931549	+	0.363616i	$0.118458\pi$
$3$	41.2346	+	71.4204i	0.293911	+	0.509069i	0.974731	−	0.223382i	$-0.0717097\pi$
$3$	41.2346	+	71.4204i	0.293911	+	0.509069i	−0.680820	+	0.732451i	$0.738376\pi$
$4$	232.691	+	403.033i	0.454474	+	0.787173i
$5$	−741.590	−	1284.47i	−0.530639	−	0.919094i	−0.999361	−	0.0357478i	$-0.988619\pi$
$5$	−741.590	−	1284.47i	−0.530639	−	0.919094i	0.468722	−	0.883346i	$-0.344715\pi$
$6$	563.079			0.177373
$7$	721.322	+	1249.37i	0.113550	+	0.196675i	0.917199	−	0.398429i	$-0.130444\pi$
$7$	721.322	+	1249.37i	0.113550	+	0.196675i	−0.803649	+	0.595104i	$0.797111\pi$
$8$	6673.32			0.576019
$9$	6440.92	−	11156.0i	0.327232	−	0.566783i
$10$	−10126.8			−0.320237
$11$	64912.9			1.33679			0.668397	−	0.743805i	$-0.266981\pi$
$11$	64912.9			1.33679			0.668397	+	0.743805i	$0.266981\pi$
$12$	−19189.8	+	33237.8i	−0.267150	+	0.462718i
$13$	1601.42	+	2773.74i	0.0155510	+	0.0269352i	0.873696	−	0.486472i	$-0.161716\pi$
$13$	1601.42	+	2773.74i	0.0155510	+	0.0269352i	−0.858145	+	0.513407i	$0.828383\pi$
$14$	9850.01			0.0685268
$15$	61158.4	−	105929.i	0.311921	−	0.540264i
$16$	−96355.9	+	166893.i	−0.367569	+	0.636648i
$17$	−313509.	+	543013.i	−0.910394	+	1.57685i	−0.0968856	+	0.995296i	$0.530888\pi$
$17$	−313509.	+	543013.i	−0.910394	+	1.57685i	−0.813508	+	0.581553i	$0.802445\pi$
$18$	−43976.9	−	76170.3i	−0.0987413	−	0.171025i
$19$	274128.	+	474804.i	0.482572	+	0.835840i	0.999800	−	0.0200082i	$-0.00636923\pi$
$19$	274128.	+	474804.i	0.482572	+	0.835840i	−0.517228	+	0.855848i	$0.673036\pi$
$20$	345123.	−	597770.i	0.482324	−	0.835409i
$21$	−59486.8	+	103034.i	−0.0667474	+	0.115610i
$22$	221605.	−	383830.i	0.201686	−	0.349331i
$23$	2.52992e6			1.88509			0.942545	−	0.334079i	$-0.108425\pi$
$23$	2.52992e6			1.88509			0.942545	+	0.334079i	$0.108425\pi$
$24$	275171.	+	476611.i	0.169298	+	0.293233i
$25$	−123350.	+	213649.i	−0.0631553	+	0.109388i
$26$	21868.1			0.00938495
$27$	2.68560e6			0.972532
$28$	−335690.	+	581432.i	−0.103211	+	0.178767i
$29$	895575.			0.235132			0.117566	−	0.993065i	$-0.462491\pi$
$29$	895575.			0.235132			0.117566	+	0.993065i	$0.462491\pi$
$30$	−417574.	−	723259.i	−0.0941212	−	0.163023i
$31$	−615101.			−0.119624			−0.0598120	−	0.998210i	$-0.519050\pi$
$31$	−615101.			−0.119624			−0.0598120	+	0.998210i	$0.519050\pi$
$32$	2.36626e6	+	4.09849e6i	0.398922	+	0.690953i
$33$	2.67666e6	+	4.63611e6i	0.392899	+	0.680520i
$34$	2.14056e6	+	3.70755e6i	0.274708	+	0.475809i
$35$	1.06985e6	−	1.85304e6i	0.120508	−	0.208727i
$36$	5.99497e6			0.594875
$37$	−8.70955e6	−	7.35564e6i	−0.763991	−	0.645227i
$37$	−8.70955e6	−	7.35564e6i	−0.763991	−	0.645227i
$38$	3.74335e6			0.291229
$39$	−132068.	+	228748.i	−0.00914125	+	0.0158331i
$40$	−4.94887e6	−	8.57169e6i	−0.305658	−	0.529415i
$41$	7.10564e6	+	1.23073e7i	0.392714	+	0.680200i	0.992806	−	0.119730i	$-0.0382030\pi$
$41$	7.10564e6	+	1.23073e7i	0.392714	+	0.680200i	−0.600093	+	0.799930i	$0.704870\pi$
$42$	406161.	+	703492.i	0.0201408	+	0.0348849i
$43$	2.99073e7			1.33404			0.667020	−	0.745040i	$-0.267570\pi$
$43$	2.99073e7			1.33404			0.667020	+	0.745040i	$0.267570\pi$
$44$	1.51047e7	+	2.61620e7i	0.607538	+	1.05229i
$45$	−1.91061e7			−0.694569
$46$	8.63684e6	−	1.49594e7i	0.284410	−	0.492612i
$47$	−6.46096e7			−1.93133			−0.965665	−	0.259790i	$-0.916347\pi$
$47$	−6.46096e7			−1.93133			−0.965665	+	0.259790i	$0.916347\pi$
$48$	−1.58928e7			−0.432130
$49$	1.91362e7	−	3.31449e7i	0.474213	−	0.821360i
$50$	842204.	+	1.45874e6i	0.0190569	+	0.0330075i
$51$	−5.17096e7			−1.07030
$52$	−745271.	+	1.29085e6i	−0.0141351	+	0.0244827i
$53$	−3.39248e7	+	5.87594e7i	−0.590575	+	1.02291i	0.403580	+	0.914945i	$0.367766\pi$
$53$	−3.39248e7	+	5.87594e7i	−0.590575	+	1.02291i	−0.994155	+	0.107962i	$0.965567\pi$
$54$	9.16828e6	−	1.58799e7i	0.146729	−	0.254142i
$55$	−4.81388e7	−	8.33789e7i	−0.709354	−	1.22864i
$56$	4.81361e6	+	8.33741e6i	0.0654071	+	0.113288i
$57$	−2.26071e7	+	3.91567e7i	−0.283667	+	0.491325i
$58$	3.05738e6	−	5.29554e6i	0.0354751	−	0.0614446i
$59$	7.11183e7	−	1.23180e8i	0.764095	−	1.32345i	−0.176629	−	0.984277i	$-0.556519\pi$
$59$	7.11183e7	−	1.23180e8i	0.764095	−	1.32345i	0.940724	−	0.339173i	$-0.110147\pi$
$60$	5.69240e7			0.567041
$61$	−2.56718e7	−	4.44648e7i	−0.237395	−	0.411180i	0.722571	−	0.691297i	$-0.242960\pi$
$61$	−2.56718e7	−	4.44648e7i	−0.237395	−	0.411180i	−0.959966	+	0.280116i	$0.909627\pi$
$62$	−2.09988e6	+	3.63709e6i	−0.0180481	+	0.0312602i
$63$	1.85839e7			0.148629
$64$	−6.63560e7			−0.494391
$65$	2.37519e6	−	4.11395e6i	0.0165040	−	0.0285857i
$66$	3.65511e7			0.237112
$67$	−1.40571e8	−	2.43477e8i	−0.852237	−	1.47612i	−0.879185	−	0.476480i	$-0.841912\pi$
$67$	−1.40571e8	−	2.43477e8i	−0.852237	−	1.47612i	0.0269486	−	0.999637i	$-0.491421\pi$
$68$	−2.91803e8			−1.65500
$69$	1.04320e8	+	1.80688e8i	0.554049	+	0.959641i
$70$	−7.30467e6	−	1.26521e7i	−0.0363630	−	0.0629825i
$71$	1.59188e8	+	2.75722e8i	0.743444	+	1.28768i	0.950918	+	0.309442i	$0.100142\pi$
$71$	1.59188e8	+	2.75722e8i	0.743444	+	1.28768i	−0.207474	+	0.978241i	$0.566524\pi$
$72$	4.29823e7	−	7.44475e7i	0.188492	−	0.326478i
$73$	−4.42164e7			−0.182235			−0.0911173	−	0.995840i	$-0.529044\pi$
$73$	−4.42164e7			−0.182235			−0.0911173	+	0.995840i	$0.529044\pi$
$74$	−7.32272e7	+	2.63884e7i	−0.283877	+	0.102299i
$75$	−2.03452e7			−0.0742483
$76$	−1.27574e8	+	2.20965e8i	−0.438634	+	0.759736i
$77$	4.68231e7	+	8.11000e7i	0.151793	+	0.262913i
$78$	901724.	+	1.56183e6i	0.00275834	+	0.00477759i
$79$	9.30295e6	+	1.61132e7i	0.0268719	+	0.0465436i	0.879149	−	0.476548i	$-0.158112\pi$
$79$	9.30295e6	+	1.61132e7i	0.0268719	+	0.0465436i	−0.852277	+	0.523091i	$0.824779\pi$
$80$	2.85826e8			0.780185
$81$	−1.60371e7	−	2.77770e7i	−0.0413945	−	0.0716973i
$82$	9.70310e7			0.237000
$83$	9.26657e6	−	1.60502e7i	0.0214322	−	0.0371217i	−0.855110	−	0.518446i	$-0.826511\pi$
$83$	9.26657e6	−	1.60502e7i	0.0214322	−	0.0371217i	0.876543	+	0.481324i	$0.159844\pi$
$84$	−5.53682e7			−0.121340
$85$	9.29980e8			1.93236
$86$	1.02100e8	−	1.76842e8i	0.201271	−	0.348612i
$87$	3.69287e7	+	6.39623e7i	0.0691078	+	0.119698i
$88$	4.33185e8			0.770018
$89$	1.56999e8	−	2.71930e8i	0.265242	−	0.459413i	−0.702385	−	0.711797i	$-0.747881\pi$
$89$	1.56999e8	−	2.71930e8i	0.265242	−	0.459413i	0.967627	+	0.252385i	$0.0812148\pi$
$90$	−6.52257e7	+	1.12974e8i	−0.104792	+	0.181505i
$91$	−2.31027e6	+	4.00151e6i	−0.00353165	+	0.00611699i
$92$	5.88690e8	+	1.01964e9i	0.856725	+	1.48389i
$93$	−2.53634e7	−	4.39308e7i	−0.0351589	−	0.0608969i
$94$	−2.20569e8	+	3.82037e8i	−0.291386	+	0.504696i
$95$	4.06582e8	−	7.04220e8i	0.512143	−	0.887058i
$96$	−1.95144e8	+	3.37999e8i	−0.234495	+	0.406158i
$97$	−6.21385e8			−0.712669			−0.356335	−	0.934358i	$-0.615974\pi$
$97$	−6.21385e8			−0.712669			−0.356335	+	0.934358i	$0.615974\pi$
$98$	−1.30657e8	−	2.26305e8i	−0.143092	−	0.247843i
$99$	4.18099e8	−	7.24168e8i	0.437442	−	0.757672i
$100$	−1.14810e8			−0.114810
$101$	−1.54700e9			−1.47926			−0.739631	−	0.673012i	$-0.765000\pi$
$101$	−1.54700e9			−1.47926			−0.739631	+	0.673012i	$0.765000\pi$
$102$	−1.76530e8	+	3.05759e8i	−0.161480	+	0.279691i
$103$	8.10069e7			0.0709177			0.0354589	−	0.999371i	$-0.488711\pi$
$103$	8.10069e7			0.0709177			0.0354589	+	0.999371i	$0.488711\pi$
$104$	1.06868e7	+	1.85100e7i	0.00895769	+	0.0155152i
$105$	1.76460e8			0.141675
$106$	2.31630e8	+	4.01194e8i	0.178204	+	0.308659i
$107$	−1.71955e7	−	2.97835e7i	−0.0126820	−	0.0219659i	0.859615	−	0.510943i	$-0.170704\pi$
$107$	−1.71955e7	−	2.97835e7i	−0.0126820	−	0.0219659i	−0.872297	+	0.488977i	$0.837370\pi$
$108$	6.24914e8	+	1.08238e9i	0.441991	+	0.765550i
$109$	−8.58265e8	+	1.48656e9i	−0.582374	+	1.00870i	0.412823	+	0.910811i	$0.364543\pi$
$109$	−8.58265e8	+	1.48656e9i	−0.582374	+	1.00870i	−0.995197	+	0.0978902i	$0.968791\pi$
$110$	−6.57359e8			−0.428091
$111$	1.66208e8	−	9.25347e8i	0.103920	−	0.578564i
$112$	−2.78015e8			−0.166950
$113$	1.20086e9	−	2.07995e9i	0.692851	−	1.20005i	−0.278048	−	0.960567i	$-0.589688\pi$
$113$	1.20086e9	−	2.07995e9i	0.692851	−	1.20005i	0.970900	−	0.239487i	$-0.0769791\pi$
$114$	1.54356e8	+	2.67352e8i	0.0855955	+	0.148256i
$115$	−1.87617e9	−	3.24962e9i	−1.00030	−	1.73257i
$116$	2.08392e8	+	3.60946e8i	0.106861	+	0.185089i
$117$	4.12584e7			0.0203552
$118$	−4.85577e8	−	8.41045e8i	−0.230563	−	0.399347i
$119$	−9.04563e8			−0.413502
$120$	4.08129e8	−	7.06900e8i	0.179673	−	0.311202i
$121$	1.85574e9			0.787016
$122$	−3.50561e8			−0.143266
$123$	−5.85997e8	+	1.01498e9i	−0.230846	+	0.399837i
$124$	−1.43128e8	−	2.47906e8i	−0.0543661	−	0.0941648i
$125$	−2.53094e9			−0.927227
$126$	6.34431e7	−	1.09887e8i	0.0224242	−	0.0388398i
$127$	2.06569e8	−	3.57789e8i	0.0704611	−	0.122042i	−0.828642	−	0.559778i	$-0.810886\pi$
$127$	2.06569e8	−	3.57789e8i	0.0704611	−	0.122042i	0.899103	+	0.437736i	$0.144220\pi$
$128$	−1.43806e9	+	2.49079e9i	−0.473512	+	0.820147i
$129$	1.23321e9	+	2.13599e9i	0.392089	+	0.679119i
$130$	−1.62172e7	−	2.80890e7i	−0.00498002	−	0.00862564i
$131$	3.05406e9	−	5.28979e9i	0.906060	−	1.56934i	0.0865718	−	0.996246i	$-0.472409\pi$
$131$	3.05406e9	−	5.28979e9i	0.906060	−	1.56934i	0.819488	−	0.573096i	$-0.194258\pi$
$132$	−1.24567e9	+	2.15756e9i	−0.357125	+	0.618558i
$133$	−3.95469e8	+	6.84973e8i	−0.109592	+	0.189820i
$134$	−1.91957e9			−0.514319
$135$	−1.99161e9	−	3.44957e9i	−0.516063	−	0.893847i
$136$	−2.09214e9	+	3.62370e9i	−0.524404	+	0.908295i
$137$	−2.59778e9			−0.630029			−0.315014	−	0.949087i	$-0.602009\pi$
$137$	−2.59778e9			−0.630029			−0.315014	+	0.949087i	$0.602009\pi$
$138$	1.42455e9			0.334365
$139$	−1.82168e9	+	3.15524e9i	−0.413910	+	0.716913i	−0.995313	−	0.0967025i	$-0.969170\pi$
$139$	−1.82168e9	+	3.15524e9i	−0.413910	+	0.716913i	0.581403	+	0.813615i	$0.302504\pi$
$140$	9.95778e8			0.219072
$141$	−2.66415e9	−	4.61444e9i	−0.567640	−	0.983181i
$142$	2.17379e9			0.448663
$143$	1.03953e8	+	1.80051e8i	0.0207885	+	0.0360068i
$144$	1.24124e9	+	2.14989e9i	0.240561	+	0.416663i
$145$	−6.64150e8	−	1.15034e9i	−0.124770	−	0.216108i
$146$	−1.50949e8	+	2.61452e8i	−0.0274943	+	0.0476216i
$147$	3.15629e9			0.557506
$148$	9.37930e8	−	5.22182e9i	0.160691	−	0.894632i
$149$	4.69876e9			0.780989			0.390495	−	0.920605i	$-0.372304\pi$
$149$	4.69876e9			0.780989			0.390495	+	0.920605i	$0.372304\pi$
$150$	−6.94559e7	+	1.20301e8i	−0.0112021	+	0.0194026i
$151$	1.57833e9	+	2.73375e9i	0.247059	+	0.427919i	0.962709	−	0.270541i	$-0.0872024\pi$
$151$	1.57833e9	+	2.73375e9i	0.247059	+	0.427919i	−0.715649	+	0.698460i	$0.753869\pi$
$152$	1.82934e9	+	3.16852e9i	0.277971	+	0.481459i
$153$	4.03857e9	+	6.99500e9i	0.595821	+	1.03199i
$154$	6.39393e8			0.0916061
$155$	4.56153e8	+	7.90080e8i	0.0634772	+	0.109946i
$156$	−1.22924e8			−0.0166179
$157$	1.05734e9	−	1.83136e9i	0.138888	−	0.240561i	−0.788188	−	0.615435i	$-0.788980\pi$
$157$	1.05734e9	−	1.83136e9i	0.138888	−	0.240561i	0.927076	+	0.374873i	$0.122314\pi$
$158$	1.27036e8			0.0162170
$159$	−5.59550e9			−0.694307
$160$	3.50960e9	−	6.07880e9i	0.423367	−	0.733293i
$161$	1.82489e9	+	3.16080e9i	0.214052	+	0.370750i
$162$	−2.18994e8			−0.0249813
$163$	3.52421e9	−	6.10411e9i	0.391037	−	0.677296i	−0.601550	−	0.798835i	$-0.705450\pi$
$163$	3.52421e9	−	6.10411e9i	0.391037	−	0.677296i	0.992587	+	0.121540i	$0.0387832\pi$
$164$	−3.30684e9	+	5.72761e9i	−0.356957	+	0.618267i
$165$	3.96997e9	−	6.87619e9i	0.416974	−	0.722221i
$166$	−6.32698e7	−	1.09586e8i	−0.00646710	−	0.0112014i
$167$	5.06647e9	+	8.77538e9i	0.504059	+	0.873055i	0.999989	+	0.00469289i	$0.00149380\pi$
$167$	5.06647e9	+	8.77538e9i	0.504059	+	0.873055i	−0.495930	+	0.868362i	$0.665173\pi$
$168$	−3.96974e8	+	6.87580e8i	−0.0384477	+	0.0665934i
$169$	5.29712e9	−	9.17488e9i	0.499516	−	0.865188i
$170$	3.17483e9	−	5.49897e9i	0.291542	−	0.504965i
$171$	7.06254e9			0.631653
$172$	6.95915e9	+	1.20536e10i	0.606287	+	1.05012i
$173$	−8.29242e9	+	1.43629e10i	−0.703840	+	1.21909i	0.263268	+	0.964723i	$0.415200\pi$
$173$	−8.29242e9	+	1.43629e10i	−0.703840	+	1.21909i	−0.967108	+	0.254364i	$0.918134\pi$
$174$	5.04279e8			0.0417061
$175$	−3.55901e8			−0.0286852
$176$	−6.25475e9	+	1.08335e10i	−0.491363	+	0.851066i
$177$	1.17301e10			0.898304
$178$	−1.07195e9	−	1.85667e9i	−0.0800359	−	0.138626i
$179$	−1.12956e9			−0.0822377			−0.0411189	−	0.999154i	$-0.513092\pi$
$179$	−1.12956e9			−0.0822377			−0.0411189	+	0.999154i	$0.513092\pi$
$180$	−4.44581e9	−	7.70037e9i	−0.315664	−	0.546746i
$181$	−1.09697e10	−	1.90000e10i	−0.759695	−	1.31583i	−0.943006	−	0.332776i	$-0.892015\pi$
$181$	−1.09697e10	−	1.90000e10i	−0.759695	−	1.31583i	0.183311	−	0.983055i	$-0.441319\pi$
$182$	1.57740e7	+	2.73213e7i	0.00106566	+	0.00184578i
$183$	2.11713e9	−	3.66698e9i	0.139546	−	0.241701i
$184$	1.68830e10			1.08585
$185$	−2.98920e9	+	1.66421e10i	−0.187621	+	1.04456i
$186$	−3.46350e8			−0.0212181
$187$	−2.03508e10	+	3.52486e10i	−1.21701	+	2.10792i
$188$	−1.50341e10	−	2.60398e10i	−0.877740	−	1.52029i
$189$	1.93718e9	+	3.35529e9i	0.110431	+	0.191272i
$190$	−2.77604e9	−	4.80823e9i	−0.154537	−	0.267667i
$191$	−2.15106e10			−1.16951			−0.584753	−	0.811211i	$-0.698809\pi$
$191$	−2.15106e10			−1.16951			−0.584753	+	0.811211i	$0.698809\pi$
$192$	−2.73616e9	−	4.73917e9i	−0.145307	−	0.251679i
$193$	−1.01777e10			−0.528010			−0.264005	−	0.964521i	$-0.585044\pi$
$193$	−1.01777e10			−0.528010			−0.264005	+	0.964521i	$0.585044\pi$
$194$	−2.12133e9	+	3.67425e9i	−0.107523	+	0.186235i
$195$	3.91760e8			0.0194028
$196$	1.78113e10			0.862070
$197$	−1.65627e8	+	2.86874e8i	−0.00783489	+	0.0135704i	−0.869916	−	0.493199i	$-0.835827\pi$
$197$	−1.65627e8	+	2.86874e8i	−0.00783489	+	0.0135704i	0.862081	+	0.506770i	$0.169161\pi$
$198$	−2.85467e9	−	4.94444e9i	−0.131997	−	0.228625i
$199$	−1.93232e9			−0.0873454			−0.0436727	−	0.999046i	$-0.513906\pi$
$199$	−1.93232e9			−0.0873454			−0.0436727	+	0.999046i	$0.513906\pi$
$200$	−8.23155e8	+	1.42575e9i	−0.0363787	+	0.0630097i
$201$	1.15928e10	−	2.00793e10i	0.500964	−	0.867695i
$202$	−5.28128e9	+	9.14744e9i	−0.223181	+	0.386561i
$203$	6.45998e8	+	1.11890e9i	0.0266992	+	0.0462444i
$204$	−1.20324e10	−	2.08407e10i	−0.486424	−	0.842511i
$205$	1.05390e10	−	1.82540e10i	0.416778	−	0.721881i
$206$	2.76547e8	−	4.78994e8i	0.0106996	−	0.0185322i
$207$	1.62950e10	−	2.82238e10i	0.616863	−	1.06844i
$208$	−6.17224e8			−0.0228643
$209$	1.77945e10	+	3.08209e10i	0.645099	+	1.11734i
$210$	6.02410e8	−	1.04341e9i	0.0213750	−	0.0370225i
$211$	−3.32245e10			−1.15395			−0.576976	−	0.816761i	$-0.695767\pi$
$211$	−3.32245e10			−1.15395			−0.576976	+	0.816761i	$0.695767\pi$
$212$	−3.15759e10			−1.07361
$213$	−1.31281e10	+	2.27386e10i	−0.437013	+	0.756929i
$214$	−2.34813e8			−0.00765350
$215$	−2.21790e10	−	3.84151e10i	−0.707894	−	1.22611i
$216$	1.79218e10			0.560196
$217$	−4.43686e8	−	7.68486e8i	−0.0135833	−	0.0235270i
$218$	5.86001e9	+	1.01498e10i	0.175729	+	0.304372i
$219$	−1.82325e9	−	3.15795e9i	−0.0535608	−	0.0927700i
$220$	2.24029e10	−	3.88030e10i	0.644767	−	1.11677i
$221$	−2.00823e9			−0.0566303
$222$	−4.90416e9	−	4.14181e9i	−0.135512	−	0.114446i
$223$	2.28012e10			0.617426			0.308713	−	0.951155i	$-0.400102\pi$
$223$	2.28012e10			0.617426			0.308713	+	0.951155i	$0.400102\pi$
$224$	−3.41367e9	+	5.91266e9i	−0.0905954	+	0.156916i
$225$	1.58898e9	+	2.75219e9i	0.0413329	+	0.0715908i
$226$	−8.19918e9	−	1.42014e10i	−0.209066	−	0.362112i
$227$	2.56687e10	+	4.44594e10i	0.641633	+	1.11134i	0.985068	+	0.172165i	$0.0550763\pi$
$227$	2.56687e10	+	4.44594e10i	0.641633	+	1.11134i	−0.343435	+	0.939177i	$0.611590\pi$
$228$	−2.10419e10			−0.515677
$229$	−1.29527e10	−	2.24348e10i	−0.311245	−	0.539091i	0.667388	−	0.744711i	$-0.267412\pi$
$229$	−1.29527e10	−	2.24348e10i	−0.311245	−	0.539091i	−0.978632	+	0.205619i	$0.934079\pi$
$230$	−2.56200e10			−0.603676
$231$	−3.86147e9	+	6.68826e9i	−0.0892274	+	0.154546i
$232$	5.97645e9			0.135440
$233$	−8.18897e10			−1.82024			−0.910118	−	0.414349i	$-0.864009\pi$
$233$	−8.18897e10			−1.82024			−0.910118	+	0.414349i	$0.864009\pi$
$234$	1.40851e8	−	2.43961e8i	0.00307106	−	0.00531923i
$235$	4.79138e10	+	8.29892e10i	1.02484	+	1.77507i
$236$	6.61943e10			1.38905
$237$	−7.67207e8	+	1.32884e9i	−0.0157959	+	0.0273593i
$238$	−3.08806e9	+	5.34868e9i	−0.0623864	+	0.108056i
$239$	−1.09908e10	+	1.90366e10i	−0.217890	+	0.377396i	−0.954163	−	0.299288i	$-0.903251\pi$
$239$	−1.09908e10	+	1.90366e10i	−0.217890	+	0.377396i	0.736273	+	0.676685i	$0.236584\pi$
$240$	1.17859e10	+	2.04139e10i	0.229305	+	0.397168i
$241$	1.86893e10	+	3.23708e10i	0.356875	+	0.618125i	0.987437	−	0.158013i	$-0.0505089\pi$
$241$	1.86893e10	+	3.23708e10i	0.356875	+	0.618125i	−0.630562	+	0.776139i	$0.717176\pi$
$242$	6.33527e9	−	1.09730e10i	0.118740	−	0.205663i
$243$	2.77529e10	−	4.80694e10i	0.510598	−	0.884382i
$244$	1.19472e10	−	2.06931e10i	0.215780	−	0.373742i
$245$	−5.67649e10			−1.00654
$246$	4.00104e9	+	6.93000e9i	0.0696570	+	0.120649i
$247$	−8.77987e8	+	1.52072e9i	−0.0150090	+	0.0259964i
$248$	−4.10476e9			−0.0689057
$249$	1.52841e9			0.0251967
$250$	−8.64029e9	+	1.49654e10i	−0.139894	+	0.242303i
$251$	1.28158e10			0.203805			0.101903	−	0.994794i	$-0.467507\pi$
$251$	1.28158e10			0.203805			0.101903	+	0.994794i	$0.467507\pi$
$252$	4.32430e9	+	7.48991e9i	0.0675482	+	0.116997i
$253$	1.64225e11			2.51998
$254$	−1.41040e9	−	2.44289e9i	−0.0212614	−	0.0368258i
$255$	3.83474e10	+	6.64196e10i	0.567943	+	0.983706i
$256$	−7.16844e9	−	1.24161e10i	−0.104315	−	0.180678i
$257$	−2.56151e10	+	4.43667e10i	−0.366267	+	0.634393i	−0.988979	−	0.148059i	$-0.952698\pi$
$257$	−2.56151e10	+	4.43667e10i	−0.366267	+	0.634393i	0.622712	+	0.782451i	$0.286031\pi$
$258$	1.68402e10			0.236623
$259$	2.90750e9	−	1.61872e10i	0.0401487	−	0.223523i
$260$	2.21074e9			0.0300025
$261$	5.76832e9	−	9.99103e9i	0.0769427	−	0.133269i
$262$	−2.08524e10	−	3.61173e10i	−0.273400	−	0.473544i
$263$	−3.01714e10	−	5.22585e10i	−0.388862	−	0.673528i	0.603435	−	0.797412i	$-0.293798\pi$
$263$	−3.01714e10	−	5.22585e10i	−0.388862	−	0.673528i	−0.992297	+	0.123884i	$0.960465\pi$
$264$	1.78622e10	+	3.09382e10i	0.226317	+	0.391992i
$265$	1.00633e11			1.25353
$266$	2.70016e9	+	4.67682e9i	0.0330691	+	0.0572774i
$267$	2.58952e10			0.311830
$268$	6.54194e10	−	1.13310e11i	0.774640	−	1.34172i
$269$	−2.92276e10			−0.340336			−0.170168	−	0.985415i	$-0.554431\pi$
$269$	−2.92276e10			−0.340336			−0.170168	+	0.985415i	$0.554431\pi$
$270$	−2.71964e10			−0.311441
$271$	−5.62533e10	+	9.74335e10i	−0.633557	+	1.09735i	0.353262	+	0.935525i	$0.385073\pi$
$271$	−5.62533e10	+	9.74335e10i	−0.633557	+	1.09735i	−0.986819	+	0.161829i	$0.948261\pi$
$272$	−6.04168e10	−	1.04645e11i	−0.669265	−	1.15920i
$273$	−3.81053e8			−0.00415196
$274$	−8.86850e9	+	1.53607e10i	−0.0950545	+	0.164639i
$275$	−8.00703e9	+	1.38686e10i	−0.0844256	+	0.146229i
$276$	−4.85488e10	+	8.40890e10i	−0.503602	+	0.872265i
$277$	7.19621e10	+	1.24642e11i	0.734420	+	1.27205i	0.954977	+	0.296679i	$0.0958792\pi$
$277$	7.19621e10	+	1.24642e11i	0.734420	+	1.27205i	−0.220557	+	0.975374i	$0.570787\pi$
$278$	1.24380e10	+	2.15432e10i	0.124896	+	0.216326i
$279$	−3.96181e9	+	6.86206e9i	−0.0391449	+	0.0678009i
$280$	7.13945e9	−	1.23659e10i	0.0694151	−	0.120230i
$281$	1.56580e10	−	2.71204e10i	0.149816	−	0.259489i	−0.781343	−	0.624101i	$-0.785465\pi$
$281$	1.56580e10	−	2.71204e10i	0.149816	−	0.259489i	0.931159	+	0.364613i	$0.118799\pi$
$282$	−3.63803e10			−0.342567
$283$	−4.81774e10	−	8.34457e10i	−0.446482	−	0.773330i	0.551672	−	0.834061i	$-0.313990\pi$
$283$	−4.81774e10	−	8.34457e10i	−0.446482	−	0.773330i	−0.998154	+	0.0607313i	$0.980657\pi$
$284$	−7.40833e10	+	1.28316e11i	−0.675753	+	1.17044i
$285$	6.70609e10			0.602099
$286$	1.41953e9			0.0125457
$287$	−1.02509e10	+	1.77551e10i	−0.0891854	+	0.154474i
$288$	6.09636e10			0.522161
$289$	−1.37281e11	−	2.37778e11i	−1.15763	−	2.00508i
$290$	−9.06929e9			−0.0752978
$291$	−2.56226e10	−	4.43796e10i	−0.209462	−	0.362798i
$292$	−1.02888e10	−	1.78207e10i	−0.0828209	−	0.143450i
$293$	−1.80668e10	−	3.12927e10i	−0.143212	−	0.248050i	0.785493	−	0.618871i	$-0.212410\pi$
$293$	−1.80668e10	−	3.12927e10i	−0.143212	−	0.248050i	−0.928704	+	0.370821i	$0.879076\pi$
$294$	1.07752e10	−	1.86632e10i	0.0841127	−	0.145688i
$295$	−2.10963e11			−1.62183
$296$	−5.81216e10	−	4.90865e10i	−0.440073	−	0.371663i
$297$	1.74330e11			1.30007
$298$	1.60410e10	−	2.77838e10i	0.117830	−	0.204088i
$299$	4.05146e9	+	7.01734e9i	0.0293151	+	0.0507753i
$300$	−4.73414e9	−	8.19978e9i	−0.0337439	−	0.0584462i
$301$	2.15728e10	+	3.73651e10i	0.151481	+	0.262372i
$302$	2.15529e10			0.149099
$303$	−6.37901e10	−	1.10488e11i	−0.434772	−	0.753047i
$304$	−1.05655e11			−0.709514
$305$	−3.80759e10	+	6.59494e10i	−0.251942	+	0.436377i
$306$	5.51486e10			0.359574
$307$	6.31095e10			0.405483			0.202741	−	0.979232i	$-0.435015\pi$
$307$	6.31095e10			0.405483			0.202741	+	0.979232i	$0.435015\pi$
$308$	−2.17906e10	+	3.77425e10i	−0.137972	+	0.238975i
$309$	3.34029e9	+	5.78555e9i	0.0208435	+	0.0361020i
$310$	6.22899e9			0.0383081
$311$	−7.69319e10	+	1.33250e11i	−0.466321	+	0.807691i	−0.999260	−	0.0384622i	$-0.987754\pi$
$311$	−7.69319e10	+	1.33250e11i	−0.466321	+	0.807691i	0.532939	+	0.846153i	$0.321087\pi$
$312$	−8.81329e8	+	1.52651e9i	−0.00526553	+	0.00912017i
$313$	2.29008e10	−	3.96653e10i	0.134865	−	0.233594i	−0.790681	−	0.612229i	$-0.790273\pi$
$313$	2.29008e10	−	3.96653e10i	0.134865	−	0.233594i	0.925546	+	0.378635i	$0.123606\pi$
$314$	−7.21923e9	−	1.25041e10i	−0.0419090	−	0.0725885i
$315$	−1.37816e10	−	2.38705e10i	−0.0788685	−	0.136604i
$316$	−4.32943e9	+	7.49879e9i	−0.0244252	+	0.0423057i
$317$	8.43524e10	−	1.46103e11i	0.469170	−	0.812627i	−0.530209	−	0.847867i	$-0.677886\pi$
$317$	8.43524e10	−	1.46103e11i	0.469170	−	0.812627i	0.999379	+	0.0352404i	$0.0112197\pi$
$318$	−1.91023e10	+	3.30862e10i	−0.104752	+	0.181436i
$319$	5.81344e10			0.314322
$320$	4.92090e10	+	8.52324e10i	0.262343	+	0.454391i
$321$	1.41810e9	−	2.45622e9i	0.00745477	−	0.0129120i
$322$	2.49198e10			0.129179
$323$	−3.43766e11			−1.75732
$324$	7.46336e9	−	1.29269e10i	0.0376255	−	0.0651692i
$325$	−7.90141e8			−0.00392852
$326$	−2.40624e10	−	4.16773e10i	−0.117994	−	0.204372i
$327$	−1.41561e11			−0.684665
$328$	4.74182e10	+	8.21307e10i	0.226210	+	0.391808i
$329$	−4.66043e10	−	8.07210e10i	−0.219303	−	0.379844i
$330$	−2.71059e10	−	4.69489e10i	−0.125821	−	0.217928i
$331$	4.42968e10	−	7.67243e10i	0.202837	−	0.351324i	−0.746605	−	0.665268i	$-0.768317\pi$
$331$	4.42968e10	−	7.67243e10i	0.202837	−	0.351324i	0.949441	+	0.313945i	$0.101651\pi$
$332$	8.62499e9			0.0389616
$333$	−1.38157e11	+	4.97866e10i	−0.615706	+	0.221878i
$334$	6.91851e10			0.304196
$335$	−2.08493e11	+	3.61120e11i	−0.904460	+	1.56657i
$336$	−1.14638e10	−	1.98559e10i	−0.0490685	−	0.0849891i
$337$	−1.00653e11	−	1.74336e11i	−0.425100	−	0.736294i	0.571330	−	0.820720i	$-0.306428\pi$
$337$	−1.00653e11	−	1.74336e11i	−0.425100	−	0.736294i	−0.996430	+	0.0844260i	$0.973094\pi$
$338$	−3.61674e10	−	6.26438e10i	−0.150727	−	0.261067i
$339$	1.98068e11			0.814547
$340$	2.16398e11	+	3.74812e11i	0.878209	+	1.52110i
$341$	−3.99280e10			−0.159913
$342$	2.41106e10	−	4.17608e10i	0.0952996	−	0.165064i
$343$	1.13429e11			0.442488
$344$	1.99581e11			0.768432
$345$	1.54726e11	−	2.67993e11i	0.588000	−	1.01845i
$346$	5.66186e10	+	9.80662e10i	0.212381	+	0.367855i
$347$	4.84779e10			0.179499			0.0897493	−	0.995964i	$-0.471393\pi$
$347$	4.84779e10			0.179499			0.0897493	+	0.995964i	$0.471393\pi$
$348$	−1.71859e10	+	2.97669e10i	−0.0628155	+	0.108800i
$349$	1.39762e11	−	2.42075e11i	0.504284	−	0.873445i	−0.495704	−	0.868491i	$-0.665090\pi$
$349$	1.39762e11	−	2.42075e11i	0.504284	−	0.873445i	0.999988	−	0.00495335i	$-0.00157671\pi$
$350$	−1.21500e9	+	2.10444e9i	−0.00432783	+	0.00749603i
$351$	4.30076e9	+	7.44913e9i	0.0151239	+	0.0261953i
$352$	1.53601e11	+	2.66045e11i	0.533276	+	0.923661i
$353$	−1.13217e11	+	1.96097e11i	−0.388083	+	0.672179i	−0.992192	−	0.124723i	$-0.960196\pi$
$353$	−1.13217e11	+	1.96097e11i	−0.388083	+	0.672179i	0.604109	+	0.796902i	$0.293529\pi$
$354$	4.00452e10	−	6.93603e10i	0.135530	−	0.234745i
$355$	2.36105e11	−	4.08946e11i	0.789001	−	1.36659i
$356$	1.46129e11			0.482183
$357$	−3.72993e10	−	6.46043e10i	−0.121533	−	0.210501i
$358$	−3.85618e9	+	6.67910e9i	−0.0124075	+	0.0214904i
$359$	4.30804e11			1.36884			0.684422	−	0.729086i	$-0.260054\pi$
$359$	4.30804e11			1.36884			0.684422	+	0.729086i	$0.260054\pi$
$360$	−1.27501e11			−0.400085
$361$	1.10514e10	−	1.91416e10i	0.0342480	−	0.0593192i
$362$	−1.49796e11			−0.458471
$363$	7.65208e10	+	1.32538e11i	0.231313	+	0.400646i
$364$	−2.15032e9			−0.00642018
$365$	3.27905e10	+	5.67948e10i	0.0967007	+	0.167491i
$366$	−1.44552e10	−	2.50372e10i	−0.0421076	−	0.0729324i
$367$	1.72016e10	+	2.97941e10i	0.0494962	+	0.0857299i	0.889712	−	0.456522i	$-0.150905\pi$
$367$	1.72016e10	+	2.97941e10i	0.0494962	+	0.0857299i	−0.840216	+	0.542252i	$0.817572\pi$
$368$	−2.43773e11	+	4.22227e11i	−0.692900	+	1.20014i
$369$	1.83067e11			0.514034
$370$	8.81997e10	+	7.44890e10i	0.244658	+	0.206626i
$371$	−9.78827e10			−0.268240
$372$	1.18037e10	−	2.04446e10i	0.0319576	−	0.0553522i
$373$	−1.73050e11	−	2.99732e11i	−0.462896	−	0.801759i	0.536208	−	0.844086i	$-0.319856\pi$
$373$	−1.73050e11	−	2.99732e11i	−0.462896	−	0.801759i	−0.999104	+	0.0423270i	$0.986523\pi$
$374$	1.38950e11	+	2.40668e11i	0.367228	+	0.636058i
$375$	−1.04362e11	−	1.80761e11i	−0.272522	−	0.472023i
$376$	−4.31160e11			−1.11248
$377$	1.43419e9	+	2.48409e9i	0.00365654	+	0.00633331i
$378$	2.64531e10			0.0666445
$379$	−1.35099e11	+	2.33998e11i	−0.336338	+	0.582554i	−0.983741	−	0.179594i	$-0.942522\pi$
$379$	−1.35099e11	+	2.33998e11i	−0.336338	+	0.582554i	0.647403	+	0.762148i	$0.275855\pi$
$380$	3.78431e11			0.931024
$381$	3.40712e10			0.0828372
$382$	−7.34345e10	+	1.27192e11i	−0.176447	+	0.305616i
$383$	1.88561e11	+	3.26597e11i	0.447772	+	0.775565i	0.998241	−	0.0592914i	$-0.0188841\pi$
$383$	1.88561e11	+	3.26597e11i	0.447772	+	0.775565i	−0.550468	+	0.834856i	$0.685551\pi$
$384$	−2.37191e11			−0.556682
$385$	6.94472e10	−	1.20286e11i	0.161095	−	0.279024i
$386$	−3.47454e10	+	6.01808e10i	−0.0796626	+	0.137980i
$387$	1.92630e11	−	3.33645e11i	0.436541	−	0.756111i
$388$	−1.44591e11	−	2.50438e11i	−0.323890	−	0.560994i
$389$	−1.01525e11	−	1.75846e11i	−0.224802	−	0.389368i	0.731458	−	0.681886i	$-0.238840\pi$
$389$	−1.01525e11	−	1.75846e11i	−0.224802	−	0.389368i	−0.956260	+	0.292518i	$0.905507\pi$
$390$	1.33742e9	−	2.31648e9i	0.00292737	−	0.00507035i
$391$	−7.93153e11	+	1.37378e12i	−1.71617	+	2.97250i
$392$	1.27702e11	−	2.21186e11i	0.273155	−	0.473119i
$393$	5.03732e11			1.06520
$394$	1.13086e9	+	1.95870e9i	0.00236415	+	0.00409483i
$395$	1.37980e10	−	2.38988e10i	0.0285186	−	0.0493956i
$396$	3.89151e11			0.795225
$397$	2.55031e11			0.515272			0.257636	−	0.966242i	$-0.417057\pi$
$397$	2.55031e11			0.515272			0.257636	+	0.966242i	$0.417057\pi$
$398$	−6.59670e9	+	1.14258e10i	−0.0131781	+	0.0228251i
$399$	−6.52281e10			−0.128842
$400$	−2.37711e10	−	4.11727e10i	−0.0464278	−	0.0804154i
$401$	6.59597e11			1.27388			0.636941	−	0.770913i	$-0.280200\pi$
$401$	6.59597e11			1.27388			0.636941	+	0.770913i	$0.280200\pi$
$402$	−7.91527e10	−	1.37097e11i	−0.151164	−	0.261824i
$403$	−9.85033e8	−	1.70613e9i	−0.00186028	−	0.00322210i
$404$	−3.59974e11	−	6.23493e11i	−0.672287	−	1.16444i
$405$	−2.37859e10	+	4.11983e10i	−0.0439310	+	0.0760908i
$406$	8.82142e9			0.0161128
$407$	−5.65363e11	−	4.77476e11i	−1.02130	−	0.862536i
$408$	−3.45075e11			−0.616513
$409$	3.36063e11	−	5.82077e11i	0.593834	−	1.02855i	−0.399876	−	0.916569i	$-0.630947\pi$
$409$	3.36063e11	−	5.82077e11i	0.593834	−	1.02855i	0.993710	−	0.111982i	$-0.0357198\pi$
$410$	−7.19573e10	−	1.24634e11i	−0.125761	−	0.217825i
$411$	−1.07119e11	−	1.85535e11i	−0.185173	−	0.320728i
$412$	1.88496e10	+	3.26484e10i	0.0322303	+	0.0558245i
$413$	2.05197e11			0.347052
$414$	−1.11258e11	−	1.92705e11i	−0.186136	−	0.322397i
$415$	−2.74880e10			−0.0454911
$416$	−7.57875e9	+	1.31268e10i	−0.0124073	+	0.0214901i
$417$	−3.00465e11			−0.486611
$418$	2.42992e11			0.389313
$419$	7.14196e10	−	1.23702e11i	0.113202	−	0.196072i	−0.803858	−	0.594822i	$-0.797223\pi$
$419$	7.14196e10	−	1.23702e11i	0.113202	−	0.196072i	0.917060	+	0.398750i	$0.130556\pi$
$420$	4.10605e10	+	7.11189e10i	0.0643877	+	0.111523i
$421$	6.51036e11			1.01003			0.505017	−	0.863110i	$-0.331486\pi$
$421$	6.51036e11			1.01003			0.505017	+	0.863110i	$0.331486\pi$
$422$	−1.13424e11	+	1.96457e11i	−0.174100	+	0.301551i
$423$	−4.16145e11	+	7.20784e11i	−0.631994	+	1.09465i
$424$	−2.26391e11	+	3.92120e11i	−0.340183	+	0.589214i
$425$	−7.73428e10	−	1.33962e11i	−0.114992	−	0.199173i
$426$	8.96355e10	+	1.55253e11i	0.131867	+	0.228401i
$427$	3.70352e10	−	6.41469e10i	0.0539125	−	0.0933792i
$428$	8.00248e9	−	1.38607e10i	0.0115273	−	0.0199659i
$429$	−8.57290e9	+	1.48487e10i	−0.0122200	+	0.0211656i
$430$	−3.02865e11			−0.427209
$431$	−3.80776e11	−	6.59523e11i	−0.531523	−	0.920624i	−0.999323	−	0.0367901i	$-0.988287\pi$
$431$	−3.80776e11	−	6.59523e11i	−0.531523	−	0.920624i	0.467800	−	0.883834i	$-0.345047\pi$
$432$	−2.58773e11	+	4.48208e11i	−0.357472	+	0.619160i
$433$	−1.17120e12			−1.60116			−0.800578	−	0.599228i	$-0.795474\pi$
$433$	−1.17120e12			−1.60116			−0.800578	+	0.599228i	$0.795474\pi$
$434$	−6.05875e9			−0.00819745
$435$	5.47719e10	−	9.48677e10i	0.0733426	−	0.127033i
$436$	−7.98842e11			−1.05870
$437$	6.93523e11	+	1.20122e12i	0.909692	+	1.57563i
$438$	−2.48973e10			−0.0323236
$439$	−6.97305e11	−	1.20777e12i	−0.896050	−	1.55200i	−0.832499	−	0.554026i	$-0.813091\pi$
$439$	−6.97305e11	−	1.20777e12i	−0.896050	−	1.55200i	−0.0635507	−	0.997979i	$-0.520242\pi$
$440$	−3.21246e11	−	5.56414e11i	−0.408602	−	0.707719i
$441$	−2.46509e11	−	4.26966e11i	−0.310356	−	0.537552i
$442$	−6.85585e9	+	1.18747e10i	−0.00854400	+	0.0147986i
$443$	−9.97467e11			−1.23050			−0.615250	−	0.788332i	$-0.710945\pi$
$443$	−9.97467e11			−1.23050			−0.615250	+	0.788332i	$0.710945\pi$
$444$	4.11620e11	−	1.48332e11i	0.502659	−	0.181139i
$445$	−4.65716e11			−0.562991
$446$	7.78402e10	−	1.34823e11i	0.0931531	−	0.161346i
$447$	1.93751e11	+	3.35587e11i	0.229541	+	0.397577i
$448$	−4.78640e10	−	8.29029e10i	−0.0561382	−	0.0972341i
$449$	−1.01443e10	−	1.75705e10i	−0.0117792	−	0.0204021i	0.860076	−	0.510166i	$-0.170416\pi$
$449$	−1.01443e10	−	1.75705e10i	−0.0117792	−	0.0204021i	−0.871855	+	0.489764i	$0.837083\pi$
$450$	2.16983e10			0.0249442
$451$	4.61248e11	+	7.98905e11i	0.524977	+	0.909287i
$452$	1.11772e12			1.25953
$453$	−1.30163e11	+	2.25450e11i	−0.145227	+	0.251541i
$454$	3.50518e11			0.387221
$455$	6.85311e9			0.00749612
$456$	−1.50864e11	+	2.61305e11i	−0.163397	+	0.283013i
$457$	−1.52475e11	−	2.64094e11i	−0.163521	−	0.283227i	0.772608	−	0.634884i	$-0.218952\pi$
$457$	−1.52475e11	−	2.64094e11i	−0.163521	−	0.283227i	−0.936129	+	0.351656i	$0.885619\pi$
$458$	−1.76876e11			−0.187834
$459$	−8.41958e11	+	1.45831e12i	−0.885387	+	1.53354i
$460$	8.73134e11	−	1.51231e12i	0.909224	−	1.57482i
$461$	9.53716e11	−	1.65188e12i	0.983478	−	1.70343i	0.334967	−	0.942230i	$-0.391275\pi$
$461$	9.53716e11	−	1.65188e12i	0.983478	−	1.70343i	0.648512	−	0.761205i	$-0.275392\pi$
$462$	2.63651e10	+	4.56657e10i	0.0269241	+	0.0466339i
$463$	1.24738e11	+	2.16052e11i	0.126149	+	0.218496i	0.922181	−	0.386758i	$-0.126405\pi$
$463$	1.24738e11	+	2.16052e11i	0.126149	+	0.218496i	−0.796033	+	0.605254i	$0.793072\pi$
$464$	−8.62939e10	+	1.49465e11i	−0.0864270	+	0.149696i
$465$	−3.76186e10	+	6.51573e10i	−0.0373133	+	0.0646286i
$466$	−2.79561e11	+	4.84214e11i	−0.274625	+	0.475665i
$467$	1.61858e11			0.157474			0.0787369	−	0.996895i	$-0.474911\pi$
$467$	1.61858e11			0.157474			0.0787369	+	0.996895i	$0.474911\pi$
$468$	9.60045e9	+	1.66285e10i	0.00925093	+	0.0160231i
$469$	2.02794e11	−	3.51250e11i	0.193543	−	0.335227i
$470$	6.54287e11			0.618483
$471$	1.74396e11			0.163283
$472$	4.74595e11	−	8.22022e11i	0.440133	−	0.762333i
$473$	1.94137e12			1.78334
$474$	5.23830e9	+	9.07299e9i	0.00476637	+	0.00825559i
$475$	−1.35255e11			−0.121908
$476$	−2.10484e11	−	3.64568e11i	−0.187926	−	0.325497i
$477$	4.37013e11	+	7.56929e11i	0.386511	+	0.669456i
$478$	7.50421e10	+	1.29977e11i	0.0657476	+	0.113878i
$479$	−3.65434e11	+	6.32950e11i	−0.317175	+	0.549363i	−0.979897	−	0.199502i	$-0.936068\pi$
$479$	−3.65434e11	+	6.32950e11i	−0.317175	+	0.549363i	0.662723	+	0.748865i	$0.269401\pi$
$480$	5.78867e11			0.497729
$481$	6.45499e9	−	3.59374e10i	0.00549848	−	0.0306122i
$482$	2.55211e11			0.215371
$483$	−1.50497e11	+	2.60669e11i	−0.125825	+	0.217935i
$484$	4.31814e11	+	7.47925e11i	0.357679	+	0.619518i
$485$	4.60813e11	+	7.98152e11i	0.378170	+	0.655010i
$486$	−1.89489e11	−	3.28205e11i	−0.154071	−	0.266859i
$487$	4.60129e11			0.370680			0.185340	−	0.982674i	$-0.440661\pi$
$487$	4.60129e11			0.370680			0.185340	+	0.982674i	$0.440661\pi$
$488$	−1.71316e11	−	2.96728e11i	−0.136744	−	0.236848i
$489$	5.81278e11			0.459720
$490$	−1.93788e11	+	3.35651e11i	−0.151860	+	0.263030i
$491$	6.15398e11			0.477847			0.238924	−	0.971038i	$-0.423205\pi$
$491$	6.15398e11			0.477847			0.238924	+	0.971038i	$0.423205\pi$
$492$	−5.45424e11			−0.419654
$493$	−2.80770e11	+	4.86309e11i	−0.214062	+	0.370767i
$494$	5.99467e9	+	1.03831e10i	0.00452892	+	0.00784431i
$495$	−1.24023e12			−0.928495
$496$	5.92686e10	−	1.02656e11i	0.0439701	−	0.0761584i
$497$	−2.29652e11	+	3.97769e11i	−0.168836	+	0.292433i
$498$	5.21781e9	−	9.03751e9i	0.00380151	−	0.00658441i
$499$	1.43660e11	+	2.48826e11i	0.103725	+	0.179657i	0.913217	−	0.407475i	$-0.133590\pi$
$499$	1.43660e11	+	2.48826e11i	0.103725	+	0.179657i	−0.809492	+	0.587131i	$0.800257\pi$
$500$	−5.88926e11	−	1.02005e12i	−0.421401	−	0.729888i
$501$	−4.17827e11	+	7.23698e11i	−0.296297	+	0.513201i
$502$	4.37517e10	−	7.57801e10i	0.0307488	−	0.0532584i
$503$	−4.54480e11	+	7.87182e11i	−0.316562	+	0.548301i	−0.979768	−	0.200135i	$-0.935862\pi$
$503$	−4.54480e11	+	7.87182e11i	−0.316562	+	0.548301i	0.663206	+	0.748437i	$0.269195\pi$
$504$	1.24016e11			0.0856132
$505$	1.14724e12	+	1.98708e12i	0.784954	+	1.35958i
$506$	5.60643e11	−	9.71061e11i	0.380197	−	0.658521i
$507$	8.73699e11			0.587254
$508$	1.92267e11			0.128091
$509$	5.00083e11	−	8.66170e11i	0.330227	−	0.571970i	−0.652329	−	0.757936i	$-0.726208\pi$
$509$	5.00083e11	−	8.66170e11i	0.330227	−	0.571970i	0.982556	+	0.185966i	$0.0595414\pi$
$510$	5.23652e11			0.342750
$511$	−3.18943e10	−	5.52425e10i	−0.0206928	−	0.0358409i
$512$	−1.57046e12			−1.00998
$513$	7.36197e11	+	1.27513e12i	0.469317	+	0.812880i
$514$	1.74894e11	+	3.02925e11i	0.110520	+	0.191426i
$515$	−6.00740e10	−	1.04051e11i	−0.0376317	−	0.0651800i
$516$	−5.73916e11	+	9.94051e11i	−0.356389	+	0.617284i
$517$	−4.19400e12			−2.58179
$518$	−8.57891e10	−	7.24531e10i	−0.0523538	−	0.0442154i
$519$	−1.36774e12			−0.827466
$520$	1.58504e10	−	2.74537e10i	0.00950660	−	0.0164659i
$521$	−5.41370e10	−	9.37681e10i	−0.0321903	−	0.0557552i	0.849481	−	0.527618i	$-0.176915\pi$
$521$	−5.41370e10	−	9.37681e10i	−0.0321903	−	0.0557552i	−0.881672	+	0.471863i	$0.843582\pi$
$522$	−3.93846e10	−	6.82162e10i	−0.0232172	−	0.0402133i
$523$	6.89731e11	+	1.19465e12i	0.403109	+	0.698205i	0.994099	−	0.108473i	$-0.0345962\pi$
$523$	6.89731e11	+	1.19465e12i	0.403109	+	0.698205i	−0.590990	+	0.806679i	$0.701263\pi$
$524$	2.84261e12			1.64712
$525$	−1.46754e10	−	2.54186e10i	−0.00843091	−	0.0146028i
$526$	−4.12006e11			−0.234675
$527$	1.92839e11	−	3.34008e11i	0.108905	−	0.188629i
$528$	−1.03165e12			−0.577669
$529$	4.59936e12			2.55357
$530$	3.43549e11	−	5.95044e11i	0.189124	−	0.327573i
$531$	−9.16133e11	−	1.58679e12i	−0.500073	−	0.866152i
$532$	−3.68088e11			−0.199228
$533$	−2.27582e10	+	3.94184e10i	−0.0122142	+	0.0211556i
$534$	8.84029e10	−	1.53118e11i	0.0470469	−	0.0814876i
$535$	−2.55040e10	+	4.41743e10i	−0.0134591	+	0.0233119i
$536$	−9.38077e11	−	1.62480e12i	−0.490904	−	0.850271i
$537$	−4.65770e10	−	8.06737e10i	−0.0241706	−	0.0418647i
$538$	−9.97794e10	+	1.72823e11i	−0.0513476	+	0.0889367i
$539$	1.24219e12	−	2.15153e12i	0.633924	−	1.09799i
$540$	9.26860e11	−	1.60537e12i	0.469075	−	0.812462i
$541$	−5.45746e11			−0.273907			−0.136953	−	0.990578i	$-0.543731\pi$
$541$	−5.45746e11			−0.273907			−0.136953	+	0.990578i	$0.543731\pi$
$542$	3.84083e11	+	6.65251e11i	0.191174	+	0.331123i
$543$	9.04659e11	−	1.56692e12i	0.446566	−	0.773475i
$544$	−2.96737e12			−1.45270
$545$	2.54592e12			1.23612
$546$	−1.30087e9	+	2.25317e9i	−0.000626420	+	0.00108499i
$547$	−2.05982e12			−0.983753			−0.491876	−	0.870665i	$-0.663689\pi$
$547$	−2.05982e12			−0.983753			−0.491876	+	0.870665i	$0.663689\pi$
$548$	−6.04481e11	−	1.04699e12i	−0.286332	−	0.495942i
$549$	−6.61399e11			−0.310733
$550$	5.46700e10	+	9.46912e10i	0.0254751	+	0.0441242i
$551$	2.45502e11	+	4.25222e11i	0.113468	+	0.196532i
$552$	6.96163e11	+	1.20579e12i	0.319143	+	0.552772i
$553$	−1.34208e10	+	2.32456e10i	−0.00610263	+	0.0105701i
$554$	9.82678e11			0.443218
$555$	−1.31184e12	+	4.72738e11i	−0.586898	+	0.211496i
$556$	−1.69555e12			−0.752446
$557$	3.69654e10	−	6.40260e10i	0.0162722	−	0.0281843i	−0.857775	−	0.514026i	$-0.828153\pi$
$557$	3.69654e10	−	6.40260e10i	0.0162722	−	0.0281843i	0.874047	+	0.485842i	$0.161487\pi$
$558$	2.70502e10	+	4.68524e10i	0.0118118	+	0.0204587i
$559$	4.78940e10	+	8.29549e10i	0.0207457	+	0.0359326i
$560$	2.06173e11	+	3.57102e11i	0.0885902	+	0.153443i
$561$	−3.35662e12			−1.43077
$562$	−1.06909e11	−	1.85171e11i	−0.0452064	−	0.0782998i
$563$	−2.24267e12			−0.940756			−0.470378	−	0.882465i	$-0.655882\pi$
$563$	−2.24267e12			−0.940756			−0.470378	+	0.882465i	$0.655882\pi$
$564$	1.23985e12	−	2.14748e12i	0.515955	−	0.893661i
$565$	−3.56219e12			−1.47062
$566$	−6.57886e11			−0.269449
$567$	2.31358e10	−	4.00723e10i	0.00940070	−	0.0162825i
$568$	1.06231e12	+	1.83998e12i	0.428238	+	0.741730i
$569$	1.61285e12			0.645043			0.322522	−	0.946562i	$-0.395470\pi$
$569$	1.61285e12			0.645043			0.322522	+	0.946562i	$0.395470\pi$
$570$	2.28937e11	−	3.96531e11i	0.0908406	−	0.157341i
$571$	4.42909e11	−	7.67140e11i	0.174362	−	0.302004i	−0.765578	−	0.643343i	$-0.777547\pi$
$571$	4.42909e11	−	7.67140e11i	0.174362	−	0.302004i	0.939940	+	0.341339i	$0.110880\pi$
$572$	−4.83777e10	+	8.37926e10i	−0.0188957	+	0.0327283i
$573$	−8.86981e11	−	1.53630e12i	−0.343731	−	0.595360i
$574$	6.99906e10	+	1.21227e11i	0.0269114	+	0.0466119i
$575$	−3.12067e11	+	5.40516e11i	−0.119054	+	0.206207i
$576$	−4.27393e11	+	7.40267e11i	−0.161781	+	0.280212i
$577$	1.47641e12	−	2.55722e12i	0.554519	−	0.960454i	−0.443422	−	0.896313i	$-0.646236\pi$
$577$	1.47641e12	−	2.55722e12i	0.554519	−	0.960454i	0.997941	−	0.0641414i	$-0.0204309\pi$
$578$	−1.87465e12			−0.698625
$579$	−4.19674e11	−	7.26897e11i	−0.155188	−	0.268794i
$580$	3.09083e11	−	5.35348e11i	0.113410	−	0.196431i
$581$	2.67367e10			0.00973454
$582$	−3.49889e11			−0.126409
$583$	−2.20216e12	+	3.81425e12i	−0.789477	+	1.36741i
$584$	−2.95070e11			−0.104971
$585$	−3.05968e10	−	5.29952e10i	−0.0108013	−	0.0187083i
$586$	−2.46712e11			−0.0864272
$587$	1.60873e12	+	2.78640e12i	0.559257	+	0.968662i	0.997559	+	0.0698338i	$0.0222469\pi$
$587$	1.60873e12	+	2.78640e12i	0.559257	+	0.968662i	−0.438301	+	0.898828i	$0.644420\pi$
$588$	7.34441e11	+	1.27209e12i	0.253372	+	0.438853i
$589$	−1.68616e11	−	2.92052e11i	−0.0577273	−	0.0999866i
$590$	−7.20199e11	+	1.24742e12i	−0.244691	+	0.423818i
$591$	−2.73182e10			−0.00921105
$592$	2.06682e12	−	7.44806e11i	0.691601	−	0.249227i
$593$	−1.28307e12			−0.426094			−0.213047	−	0.977042i	$-0.568339\pi$
$593$	−1.28307e12			−0.426094			−0.213047	+	0.977042i	$0.568339\pi$
$594$	5.95140e11	−	1.03081e12i	0.196146	−	0.339735i
$595$	6.70815e11	+	1.16189e12i	0.219420	+	0.380047i
$596$	1.09336e12	+	1.89375e12i	0.354940	+	0.614773i
$597$	−7.96785e10	−	1.38007e11i	−0.0256718	−	0.0444649i
$598$	5.53247e10			0.0176915
$599$	−4.64506e11	−	8.04547e11i	−0.147425	−	0.255347i	0.782850	−	0.622210i	$-0.213765\pi$
$599$	−4.64506e11	−	8.04547e11i	−0.147425	−	0.255347i	−0.930275	+	0.366863i	$0.880432\pi$
$600$	−1.35770e11			−0.0427684
$601$	2.57570e12	−	4.46124e12i	0.805304	−	1.39483i	−0.110782	−	0.993845i	$-0.535336\pi$
$601$	2.57570e12	−	4.46124e12i	0.805304	−	1.39483i	0.916086	−	0.400982i	$-0.131331\pi$
$602$	2.94587e11			0.0914175
$603$	−3.62163e12			−1.11552
$604$	−7.34525e11	+	1.27224e12i	−0.224564	+	0.388957i
$605$	−1.37620e12	−	2.38365e12i	−0.417621	−	0.723341i
$606$	−8.71085e11			−0.262382
$607$	2.35671e12	−	4.08195e12i	0.704624	−	1.22045i	−0.262202	−	0.965013i	$-0.584449\pi$
$607$	2.35671e12	−	4.08195e12i	0.704624	−	1.22045i	0.966827	−	0.255432i	$-0.0822178\pi$
$608$	−1.29732e12	+	2.24702e12i	−0.385017	+	0.666870i
$609$	−5.32749e10	+	9.22749e10i	−0.0156944	+	0.0271835i
$610$	2.59972e11	+	4.50286e11i	0.0760227	+	0.131675i
$611$	−1.03467e11	−	1.79210e11i	−0.0300342	−	0.0520207i
$612$	−1.87948e12	+	3.25535e12i	−0.541571	+	0.938028i
$613$	−1.35535e12	+	2.34753e12i	−0.387684	+	0.671489i	−0.992138	−	0.125152i	$-0.960058\pi$
$613$	−1.35535e12	+	2.34753e12i	−0.387684	+	0.671489i	0.604453	+	0.796641i	$0.293392\pi$
$614$	2.15448e11	−	3.73167e11i	0.0611765	−	0.105961i
$615$	1.73828e12			0.489983
$616$	3.12465e11	+	5.41206e11i	0.0874357	+	0.151443i
$617$	9.13641e11	−	1.58247e12i	0.253800	−	0.439595i	−0.710769	−	0.703426i	$-0.751653\pi$
$617$	9.13641e11	−	1.58247e12i	0.253800	−	0.439595i	0.964569	+	0.263831i	$0.0849860\pi$
$618$	4.56133e10			0.0125789
$619$	2.35366e12			0.644371			0.322185	−	0.946677i	$-0.395583\pi$
$619$	2.35366e12			0.644371			0.322185	+	0.946677i	$0.395583\pi$
$620$	−2.12285e11	+	3.67689e11i	−0.0576975	+	0.0999350i
$621$	6.79435e12			1.83331
$622$	5.25272e11	+	9.09797e11i	0.140711	+	0.243718i
$623$	4.52988e11			0.120473
$624$	−2.54510e10	−	4.40824e10i	−0.00672007	−	0.0116395i
$625$	2.11784e12	+	3.66820e12i	0.555178	+	0.961597i
$626$	−1.56361e11	−	2.70824e11i	−0.0406951	−	0.0704861i
$627$	−1.46750e12	+	2.54178e12i	−0.379204	+	0.656800i
$628$	9.84131e11			0.252484
$629$	6.72473e12	−	2.42334e12i	1.71296	−	0.617286i
$630$	−1.88195e11			−0.0475966
$631$	−2.36407e12	+	4.09468e12i	−0.593646	+	1.02822i	0.400091	+	0.916476i	$0.368979\pi$
$631$	−2.36407e12	+	4.09468e12i	−0.593646	+	1.02822i	−0.993736	+	0.111749i	$0.964355\pi$
$632$	6.20815e10	+	1.07528e11i	0.0154787	+	0.0268100i
$633$	−1.37000e12	−	2.37291e12i	−0.339159	−	0.587441i
$634$	−5.75936e11	−	9.97551e11i	−0.141571	−	0.245207i
$635$	−6.12760e11			−0.149558
$636$	−1.30202e12	−	2.25517e12i	−0.315545	−	0.546540i
$637$	1.22580e11			0.0294980
$638$	1.98463e11	−	3.43749e11i	0.0474228	−	0.0821387i
$639$	4.10127e12			0.973116
$640$	4.26580e12			1.00506
$641$	3.60105e11	−	6.23721e11i	0.0842497	−	0.145925i	−0.820822	−	0.571185i	$-0.806484\pi$
$641$	3.60105e11	−	6.23721e11i	0.0842497	−	0.145925i	0.905071	+	0.425260i	$0.139817\pi$
$642$	−9.68242e9	−	1.67705e10i	−0.00224945	−	0.00389616i
$643$	−3.91474e12			−0.903136			−0.451568	−	0.892237i	$-0.649135\pi$
$643$	−3.91474e12			−0.903136			−0.451568	+	0.892237i	$0.649135\pi$
$644$	−8.49271e11	+	1.47098e12i	−0.194563	+	0.336993i
$645$	1.82908e12	−	3.16806e12i	0.416116	−	0.720734i
$646$	−1.17357e12	+	2.03269e12i	−0.265133	+	0.459224i
$647$	2.35357e12	+	4.07651e12i	0.528030	+	0.914575i	0.999466	+	0.0326747i	$0.0104025\pi$
$647$	2.35357e12	+	4.07651e12i	0.528030	+	0.914575i	−0.471436	+	0.881900i	$0.656264\pi$
$648$	−1.07020e11	−	1.85365e11i	−0.0238440	−	0.0412990i
$649$	4.61650e12	−	7.99601e12i	1.02144	−	1.76918i
$650$	−2.69744e9	+	4.67211e9i	−0.000592709	+	0.00102660i
$651$	3.65904e10	−	6.33764e10i	0.00798459	−	0.0138297i
$652$	3.28021e12			0.710865
$653$	1.76081e12	+	3.04981e12i	0.378968	+	0.656391i	0.990912	−	0.134509i	$-0.0429458\pi$
$653$	1.76081e12	+	3.04981e12i	0.378968	+	0.656391i	−0.611945	+	0.790901i	$0.709612\pi$
$654$	−4.83271e11	+	8.37049e11i	−0.103298	+	0.178917i
$655$	−9.05945e12			−1.92316
$656$	−2.73868e12			−0.577397
$657$	−2.84794e11	+	4.93278e11i	−0.0596330	+	0.103287i
$658$	−6.36405e11			−0.132348
$659$	2.63656e12	+	4.56666e12i	0.544570	+	0.943222i	0.998634	+	0.0522535i	$0.0166404\pi$
$659$	2.63656e12	+	4.56666e12i	0.544570	+	0.943222i	−0.454064	+	0.890969i	$0.650026\pi$
$660$	3.69510e12			0.758017
$661$	−1.70322e12	−	2.95006e12i	−0.347028	−	0.601069i	0.638692	−	0.769462i	$-0.279476\pi$
$661$	−1.70322e12	−	2.95006e12i	−0.347028	−	0.601069i	−0.985720	+	0.168393i	$0.946142\pi$
$662$	−3.02447e11	−	5.23854e11i	−0.0612053	−	0.106011i
$663$	−8.28087e10	−	1.43429e11i	−0.0166443	−	0.0288287i
$664$	6.18387e10	−	1.07108e11i	0.0123454	−	0.0213828i
$665$	1.17310e12			0.232616
$666$	−1.77262e11	+	9.86887e11i	−0.0349126	+	0.194372i
$667$	2.26574e12			0.443244
$668$	−2.35784e12	+	4.08390e12i	−0.458164	+	0.793563i
$669$	9.40197e11	+	1.62847e12i	0.181468	+	0.314313i
$670$	1.42354e12	+	2.46564e12i	0.272918	+	0.472707i
$671$	−1.66643e12	−	2.88634e12i	−0.317348	−	0.549663i
$672$	−5.63046e11			−0.106508
$673$	−4.06773e12	−	7.04552e12i	−0.764336	−	1.32387i	−0.940597	−	0.339526i	$-0.889733\pi$
$673$	−4.06773e12	−	7.04552e12i	−0.764336	−	1.32387i	0.176261	−	0.984344i	$-0.443600\pi$
$674$	−1.37446e12			−0.256545
$675$	−3.31269e11	+	5.73775e11i	−0.0614206	+	0.106384i
$676$	4.93037e12			0.908070
$677$	−8.01005e12			−1.46550			−0.732751	−	0.680497i	$-0.761764\pi$
$677$	−8.01005e12			−1.46550			−0.732751	+	0.680497i	$0.761764\pi$
$678$	6.76180e11	−	1.17118e12i	0.122893	−	0.212858i
$679$	−4.48219e11	−	7.76338e11i	−0.0809238	−	0.140164i
$680$	6.20605e12			1.11308
$681$	−2.11687e12	+	3.66653e12i	−0.377167	+	0.653272i
$682$	−1.36309e11	+	2.36094e11i	−0.0241265	+	0.0417884i
$683$	3.37676e12	−	5.84871e12i	0.593754	−	1.02841i	−0.399967	−	0.916529i	$-0.630979\pi$
$683$	3.37676e12	−	5.84871e12i	0.593754	−	1.02841i	0.993721	−	0.111883i	$-0.0356881\pi$
$684$	1.64339e12	+	2.84643e12i	0.287070	+	0.497220i
$685$	1.92649e12	+	3.33678e12i	0.334318	+	0.579056i
$686$	3.87233e11	−	6.70708e11i	0.0667597	−	0.115631i
$687$	1.06820e12	−	1.85018e12i	0.182957	−	0.316890i
$688$	−2.88174e12	+	4.99133e12i	−0.490351	+	0.849313i
$689$	−2.17311e11			−0.0367363
$690$	−1.05643e12	−	1.82979e12i	−0.177427	−	0.307313i
$691$	−2.67578e12	+	4.63459e12i	−0.446477	+	0.773321i	−0.998154	−	0.0607371i	$-0.980655\pi$
$691$	−2.67578e12	+	4.63459e12i	−0.446477	+	0.773321i	0.551677	+	0.834058i	$0.313988\pi$
$692$	−7.71829e12			−1.27951
$693$	1.20634e12			0.198687
$694$	1.65497e11	−	2.86650e11i	0.0270816	−	0.0469066i
$695$	5.40377e12			0.878547
$696$	2.46437e11	+	4.26841e11i	0.0398074	+	0.0689484i
$697$	−8.91072e12			−1.43010
$698$	−9.54260e11	−	1.65283e12i	−0.152166	−	0.263559i
$699$	−3.37669e12	−	5.84860e12i	−0.534988	−	0.926626i
$700$	−8.28149e10	−	1.43440e11i	−0.0130367	−	0.0225802i
$701$	−1.46024e11	+	2.52920e11i	−0.0228398	+	0.0395596i	−0.877219	−	0.480090i	$-0.840604\pi$
$701$	−1.46024e11	+	2.52920e11i	−0.0228398	+	0.0395596i	0.854380	+	0.519649i	$0.173937\pi$
$702$	5.87290e10			0.00912716
$703$	1.10495e12	−	6.15172e12i	0.170626	−	0.949943i
$704$	−4.30736e12			−0.660898
$705$	−3.95142e12	+	6.84405e12i	−0.602423	+	1.04343i
$706$	7.73015e11	+	1.33890e12i	0.117103	+	0.202828i
$707$	−1.11589e12	−	1.93277e12i	−0.167971	−	0.290934i
$708$	2.72950e12	+	4.72763e12i	0.408256	+	0.707121i
$709$	−6.21226e11			−0.0923297			−0.0461649	−	0.998934i	$-0.514700\pi$
$709$	−6.21226e11			−0.0923297			−0.0461649	+	0.998934i	$0.514700\pi$
$710$	−1.61206e12	−	2.79218e12i	−0.238078	−	0.412364i
$711$	2.39678e11			0.0351735
$712$	1.04770e12	−	1.81468e12i	0.152784	−	0.264630i
$713$	−1.55616e12			−0.225502
$714$	−5.09340e11			−0.0733442
$715$	1.54181e11	−	2.67049e11i	0.0220624	−	0.0382132i
$716$	−2.62839e11	−	4.55250e11i	−0.0373749	−	0.0647353i
$717$	−1.81280e12			−0.256161
$718$	1.47071e12	−	2.54734e12i	0.206522	−	0.357707i
$719$	3.11398e12	−	5.39358e12i	0.434546	−	0.752657i	−0.562712	−	0.826653i	$-0.690242\pi$
$719$	3.11398e12	−	5.39358e12i	0.434546	−	0.752657i	0.997259	+	0.0739964i	$0.0235753\pi$
$720$	1.84098e12	−	3.18868e12i	0.255302	−	0.442196i
$721$	5.84321e10	+	1.01207e11i	0.00805272	+	0.0139477i
$722$	−7.54561e10	−	1.30694e11i	−0.0103342	−	0.0178994i
$723$	−1.54129e12	+	2.66959e12i	−0.209779	+	0.363348i
$724$	5.10508e12	−	8.84226e12i	0.690524	−	1.19602i
$725$	−1.10469e11	+	1.91339e11i	−0.0148498	+	0.0257206i
$726$	1.04493e12			0.139596
$727$	−1.04559e12	−	1.81102e12i	−0.138822	−	0.240446i	0.788229	−	0.615382i	$-0.210998\pi$
$727$	−1.04559e12	−	1.81102e12i	−0.138822	−	0.240446i	−0.927051	+	0.374936i	$0.877665\pi$
$728$	−1.54172e10	+	2.67034e10i	−0.00203430	+	0.00352350i
$729$	3.94620e12			0.517493
$730$	4.47770e11			0.0583582
$731$	−9.37619e12	+	1.62400e13i	−1.21450	+	2.10358i
$732$	1.97055e12			0.253681
$733$	−4.96747e11	−	8.60390e11i	−0.0635575	−	0.110085i	0.832496	−	0.554032i	$-0.186911\pi$
$733$	−4.96747e11	−	8.60390e11i	−0.0635575	−	0.110085i	−0.896053	+	0.443947i	$0.853578\pi$
$734$	2.34896e11			0.0298706
$735$	−2.34068e12	−	4.05417e12i	−0.295834	−	0.512400i
$736$	5.98646e12	+	1.03689e13i	0.752004	+	1.30251i
$737$	−9.12490e12	−	1.58048e13i	−1.13926	−	1.97326i
$738$	6.24969e11	−	1.08248e12i	0.0775541	−	0.134328i
$739$	1.26307e13			1.55786			0.778929	−	0.627112i	$-0.215763\pi$
$739$	1.26307e13			1.55786			0.778929	+	0.627112i	$0.215763\pi$
$740$	−7.40285e12	+	2.66771e12i	−0.907520	+	0.327036i
$741$	−1.44814e11			−0.0176453
$742$	−3.34159e11	+	5.78781e11i	−0.0404702	+	0.0700965i
$743$	1.68038e12	+	2.91050e12i	0.202282	+	0.350363i	0.949263	−	0.314482i	$-0.101831\pi$
$743$	1.68038e12	+	2.91050e12i	0.202282	+	0.350363i	−0.746981	+	0.664845i	$0.768498\pi$
$744$	−1.69258e11	−	2.93164e11i	−0.0202522	−	0.0350778i
$745$	−3.48455e12	−	6.03543e12i	−0.414423	−	0.717802i
$746$	−2.36309e12			−0.279354
$747$	−1.19370e11	−	2.06756e11i	−0.0140266	−	0.0242949i
$748$	−1.89418e13			−2.21240
$749$	2.48070e10	−	4.29670e10i	0.00288009	−	0.00498846i
$750$	−1.42512e12			−0.164465
$751$	1.03438e12			0.118659			0.0593293	−	0.998238i	$-0.481104\pi$
$751$	1.03438e12			0.118659			0.0593293	+	0.998238i	$0.481104\pi$
$752$	6.22551e12	−	1.07829e13i	0.709896	−	1.22958i
$753$	5.28456e11	+	9.15313e11i	0.0599006	+	0.103751i
$754$	1.95846e10			0.00220670
$755$	2.34095e12	−	4.05464e12i	0.262199	−	0.454141i
$756$	−9.01528e11	+	1.56149e12i	−0.100376	+	0.173857i
$757$	−5.50106e12	+	9.52811e12i	−0.608856	+	1.05457i	0.382573	+	0.923925i	$0.375038\pi$
$757$	−5.50106e12	+	9.52811e12i	−0.608856	+	1.05457i	−0.991429	+	0.130645i	$0.958295\pi$
$758$	9.22421e11	+	1.59768e12i	0.101489	+	0.175784i
$759$	6.77174e12	+	1.17290e13i	0.740649	+	1.28284i
$760$	2.71325e12	−	4.69948e12i	0.295004	−	0.510962i
$761$	−3.98306e12	+	6.89887e12i	−0.430513	+	0.745670i	−0.996917	−	0.0784570i	$-0.975001\pi$
$761$	−3.98306e12	+	6.89887e12i	−0.430513	+	0.745670i	0.566405	+	0.824127i	$0.308334\pi$
$762$	1.16315e11	−	2.01463e11i	0.0124979	−	0.0216470i
$763$	−2.47634e12			−0.264515
$764$	−5.00532e12	−	8.66948e12i	−0.531511	−	0.920604i
$765$	5.98992e12	−	1.03749e13i	0.632331	−	1.09523i
$766$	2.57489e12			0.270228
$767$	4.55560e11			0.0475299
$768$	5.91176e11	−	1.02395e12i	0.0613184	−	0.106207i
$769$	1.90372e12			0.196307			0.0981533	−	0.995171i	$-0.468706\pi$
$769$	1.90372e12			0.196307			0.0981533	+	0.995171i	$0.468706\pi$
$770$	−4.74168e11	−	8.21282e11i	−0.0486098	−	0.0841946i
$771$	−4.22492e12			−0.430600
$772$	−2.36826e12	−	4.10195e12i	−0.239967	−	0.415635i
$773$	5.74148e12	+	9.94453e12i	0.578384	+	1.00179i	0.995665	+	0.0930124i	$0.0296496\pi$
$773$	5.74148e12	+	9.94453e12i	0.578384	+	1.00179i	−0.417281	+	0.908777i	$0.637017\pi$
$774$	−1.31523e12	−	2.27805e12i	−0.131725	−	0.228154i
$775$	7.58728e10	−	1.31416e11i	0.00755490	−	0.0130855i
$776$	−4.14670e12			−0.410511
$777$	1.27599e12	−	4.59818e11i	0.125589	−	0.0452576i
$778$	−1.38637e12			−0.135666
$779$	−3.89571e12	+	6.74757e12i	−0.379025	+	0.656491i
$780$	9.11591e10	+	1.57892e11i	0.00881808	+	0.0152734i
$781$	1.03334e13	+	1.78979e13i	0.993831	+	1.72137i
$782$	5.41545e12	+	9.37983e12i	0.517850	+	0.896942i
$783$	2.40515e12			0.228673
$784$	3.68777e12	+	6.38741e12i	0.348611	+	0.603813i
$785$	−3.13644e12			−0.294798
$786$	1.71968e12	−	2.97857e12i	0.160711	−	0.278360i
$787$	4.89876e12			0.455198			0.227599	−	0.973755i	$-0.426913\pi$
$787$	4.89876e12			0.455198			0.227599	+	0.973755i	$0.426913\pi$
$788$	−1.54159e11			−0.0142430
$789$	2.48821e12	−	4.30971e12i	0.228582	−	0.395915i
$790$	−9.42090e10	−	1.63175e11i	−0.00860539	−	0.0149050i
$791$	3.46483e12			0.314694
$792$	2.79010e12	−	4.83260e12i	0.251975	−	0.436433i
$793$	8.22224e10	−	1.42413e11i	0.00738348	−	0.0127886i
$794$	8.70644e11	−	1.50800e12i	0.0777407	−	0.134651i
$795$	4.14957e12	+	7.18726e12i	0.368426	+	0.638133i
$796$	−4.49633e11	−	7.78788e11i	−0.0396963	−	0.0687560i
$797$	−5.69429e12	+	9.86281e12i	−0.499893	+	0.865841i	−1.00000		0.000122974i	$-0.999961\pi$
$797$	−5.69429e12	+	9.86281e12i	−0.499893	+	0.865841i	0.500106	+	0.865964i	$0.333294\pi$
$798$	−2.22680e11	+	3.85694e11i	−0.0194388	+	0.0336689i
$799$	2.02557e13	−	3.50838e13i	1.75827	−	3.04542i
$800$	−1.16752e12			−0.100776
$801$	−2.02244e12	−	3.50296e12i	−0.173592	−	0.300669i
$802$	2.25178e12	−	3.90020e12i	0.192195	−	0.332891i
$803$	−2.87022e12			−0.243610
$804$	1.07902e13			0.910701
$805$	2.70664e12	−	4.68804e12i	0.227169	−	0.393468i
$806$	−1.34511e10			−0.00112267
$807$	−1.20519e12	−	2.08745e12i	−0.100029	−	0.173255i
$808$	−1.03236e13			−0.852083
$809$	1.09563e13	+	1.89768e13i	0.899279	+	1.55760i	0.828418	+	0.560110i	$0.189241\pi$
$809$	1.09563e13	+	1.89768e13i	0.899279	+	1.55760i	0.0708609	+	0.997486i	$0.477425\pi$
$810$	1.62404e11	+	2.81292e11i	0.0132560	+	0.0229601i
$811$	−3.50042e11	−	6.06290e11i	−0.0284136	−	0.0492138i	0.851469	−	0.524405i	$-0.175712\pi$
$811$	−3.50042e11	−	6.06290e11i	−0.0284136	−	0.0492138i	−0.879883	+	0.475191i	$0.842379\pi$
$812$	−3.00636e11	+	5.20716e11i	−0.0242682	+	0.0420338i
$813$	−9.27832e12			−0.744838
$814$	−4.75339e12	+	1.71295e12i	−0.379484	+	0.136752i
$815$	−1.04541e13			−0.829997
$816$	4.98253e12	−	8.62999e12i	0.393409	−	0.681404i
$817$	8.19843e12	+	1.42001e13i	0.643771	+	1.11504i
$818$	−2.29455e12	−	3.97428e12i	−0.179187	−	0.310362i
$819$	2.97606e10	+	5.15468e10i	0.00231134	+	0.00400336i
$820$	9.80928e12			0.757660
$821$	2.51819e12	+	4.36164e12i	0.193439	+	0.335047i	0.946388	−	0.323033i	$-0.104702\pi$
$821$	2.51819e12	+	4.36164e12i	0.193439	+	0.335047i	−0.752949	+	0.658079i	$0.771369\pi$
$822$	−1.46276e12			−0.111750
$823$	−1.20787e12	+	2.09209e12i	−0.0917740	+	0.158957i	−0.908258	−	0.418411i	$-0.862587\pi$
$823$	−1.20787e12	+	2.09209e12i	−0.0917740	+	0.158957i	0.816484	+	0.577369i	$0.195920\pi$
$824$	5.40585e11			0.0408499
$825$	−1.32067e12			−0.0992546
$826$	7.00515e11	−	1.21333e12i	0.0523609	−	0.0906918i
$827$	1.22586e13	+	2.12325e13i	0.911308	+	1.57843i	0.812219	+	0.583353i	$0.198260\pi$
$827$	1.22586e13	+	2.12325e13i	0.911308	+	1.57843i	0.0990889	+	0.995079i	$0.468407\pi$
$828$	1.51668e13			1.12139
$829$	−6.42255e12	+	1.11242e13i	−0.472293	+	0.818036i	−0.999497	−	0.0317027i	$-0.989907\pi$
$829$	−6.42255e12	+	1.11242e13i	−0.472293	+	0.818036i	0.527204	+	0.849739i	$0.323240\pi$
$830$	−9.38405e10	+	1.62537e11i	−0.00686339	+	0.0118877i
$831$	−5.93466e12	+	1.02791e13i	−0.431709	+	0.747742i
$832$	−1.06264e11	−	1.84054e11i	−0.00768829	−	0.0133165i
$833$	1.19987e13	+	2.07824e13i	0.863441	+	1.49552i
$834$	−1.02575e12	+	1.77665e12i	−0.0734166	+	0.127161i
$835$	7.51449e12	−	1.30155e13i	0.534946	−	0.926554i
$836$	−8.28122e12	+	1.43435e13i	−0.586362	+	1.01561i
$837$	−1.65191e12			−0.116338
$838$	−4.87635e11	−	8.44609e11i	−0.0341584	−	0.0591640i
$839$	1.26767e13	−	2.19567e13i	0.883237	−	1.52981i	0.0355159	−	0.999369i	$-0.488693\pi$
$839$	1.26767e13	−	2.19567e13i	0.883237	−	1.52981i	0.847721	−	0.530442i	$-0.177974\pi$
$840$	1.17757e12			0.0816075
$841$	−1.37051e13			−0.944713
$842$	2.22255e12	−	3.84958e12i	0.152387	−	0.263942i
$843$	2.58260e12			0.176130
$844$	−7.73104e12	−	1.33906e13i	−0.524441	−	0.908359i
$845$	−1.57132e13			−1.06025
$846$	2.84133e12	+	4.92133e12i	0.190702	+	0.330305i
$847$	1.33859e12	+	2.31850e12i	0.0893658	+	0.154786i
$848$	−6.53770e12	−	1.13236e13i	−0.434154	−	0.751977i
$849$	3.97315e12	−	6.88170e12i	0.262452	−	0.454581i
$850$	−1.05615e12			−0.0693972
$851$	−2.20345e13	−	1.86092e13i	−1.44019	−	1.21631i
$852$	−1.22192e13			−0.794445
$853$	−7.35635e12	+	1.27416e13i	−0.475764	+	0.824048i	−0.999615	−	0.0277627i	$-0.991162\pi$
$853$	−7.35635e12	+	1.27416e13i	−0.475764	+	0.824048i	0.523850	+	0.851810i	$0.324495\pi$
$854$	−2.52867e11	−	4.37979e11i	−0.0162679	−	0.0281769i
$855$	−5.23751e12	−	9.07164e12i	−0.335180	−	0.580548i
$856$	−1.14751e11	−	1.98755e11i	−0.00730507	−	0.0126528i
$857$	2.57782e11			0.0163245			0.00816223	−	0.999967i	$-0.497402\pi$
$857$	2.57782e11			0.0163245			0.00816223	+	0.999967i	$0.497402\pi$
$858$	5.85336e10	+	1.01383e11i	0.00368733	+	0.00638665i
$859$	8.64764e12			0.541912			0.270956	−	0.962592i	$-0.412660\pi$
$859$	8.64764e12			0.541912			0.270956	+	0.962592i	$0.412660\pi$
$860$	1.03217e13	−	1.78777e13i	0.643439	−	1.11447i
$861$	−1.69077e12			−0.104850
$862$	−5.19968e12			−0.320770
$863$	−1.17513e13	+	2.03539e13i	−0.721172	+	1.24911i	0.239358	+	0.970931i	$0.423063\pi$
$863$	−1.17513e13	+	2.03539e13i	−0.721172	+	1.24911i	−0.960530	+	0.278176i	$0.910270\pi$
$864$	6.35482e12	+	1.10069e13i	0.387964	+	0.671974i
$865$	2.45983e13			1.49394
$866$	−3.99831e12	+	6.92528e12i	−0.241572	+	0.418415i
$867$	1.13215e13	−	1.96094e13i	0.680484	−	1.17863i
$868$	2.06483e11	−	3.57639e11i	0.0123466	−	0.0213849i
$869$	6.03882e11	+	1.04595e12i	0.0359222	+	0.0622191i
$870$	−3.73969e11	−	6.47733e11i	−0.0221309	−	0.0383318i
$871$	4.50227e11	−	7.79816e11i	0.0265063	−	0.0459103i
$872$	−5.72747e12	+	9.92027e12i	−0.335458	+	0.581031i
$873$	−4.00229e12	+	6.93217e12i	−0.233209	+	0.403929i
$874$	9.47040e12			0.548993
$875$	−1.82562e12	−	3.16207e12i	−0.105287	−	0.182362i
$876$	8.48506e11	−	1.46965e12i	0.0486840	−	0.0843232i
$877$	−1.33531e13			−0.762224			−0.381112	−	0.924529i	$-0.624459\pi$
$877$	−1.33531e13			−0.762224			−0.381112	+	0.924529i	$0.624459\pi$
$878$	−9.52204e12			−0.540760
$879$	1.48996e12	−	2.58068e12i	0.0841829	−	0.145809i
$880$	1.85538e13			1.04295
$881$	3.96385e12	+	6.86559e12i	0.221680	+	0.383960i	0.955318	−	0.295580i	$-0.0955127\pi$
$881$	3.96385e12	+	6.86559e12i	0.221680	+	0.383960i	−0.733638	+	0.679540i	$0.762179\pi$
$882$	−3.36620e12			−0.187297
$883$	−1.30948e13	−	2.26808e13i	−0.724894	−	1.25555i	−0.959018	−	0.283346i	$-0.908556\pi$
$883$	−1.30948e13	−	2.26808e13i	−0.724894	−	1.25555i	0.234124	−	0.972207i	$-0.424778\pi$
$884$	−4.67298e11	−	8.09383e11i	−0.0257370	−	0.0445778i
$885$	−8.69896e12	−	1.50670e13i	−0.476675	−	0.825625i
$886$	−3.40523e12	+	5.89802e12i	−0.185650	+	0.321555i
$887$	−1.47053e12			−0.0797660			−0.0398830	−	0.999204i	$-0.512699\pi$
$887$	−1.47053e12			−0.0797660			−0.0398830	+	0.999204i	$0.512699\pi$
$888$	1.10916e12	−	6.17513e12i	0.0598599	−	0.333264i
$889$	5.96012e11			0.0320035
$890$	−1.58990e12	+	2.75378e12i	−0.0849403	+	0.147121i
$891$	−1.04101e12	−	1.80309e12i	−0.0553358	−	0.0958445i
$892$	5.30562e12	+	9.18961e12i	0.280604	+	0.486021i
$893$	−1.77113e13	−	3.06769e13i	−0.932006	−	1.61428i
$894$	2.64577e12			0.138527
$895$	8.37672e11	+	1.45089e12i	0.0436385	+	0.0755842i
$896$	−4.14921e12			−0.215070
$897$	−3.34121e11	+	5.78715e11i	−0.0172321	+	0.0298468i
$898$	−1.38526e11			−0.00710866
$899$	−5.50869e11			−0.0281274
$900$	−7.39481e11	+	1.28082e12i	−0.0375695	+	0.0650724i
$901$	−2.12714e13	−	3.68432e13i	−1.07531	−	1.86250i
$902$	6.29857e12			0.316820
$903$	−1.77909e12	+	3.08147e12i	−0.0890437	+	0.154228i
$904$	8.01373e12	−	1.38802e13i	0.399095	−	0.691254i
$905$	−1.62700e13	+	2.81804e13i	−0.806248	+	1.39646i
$906$	8.88723e11	+	1.53931e12i	0.0438217	+	0.0759015i
$907$	6.06855e12	+	1.05110e13i	0.297750	+	0.515719i	0.975621	−	0.219462i	$-0.0704303\pi$
$907$	6.06855e12	+	1.05110e13i	0.297750	+	0.515719i	−0.677871	+	0.735181i	$0.737097\pi$
$908$	−1.19457e13	+	2.06906e13i	−0.583212	+	1.01015i
$909$	−9.96412e12	+	1.72584e13i	−0.484063	+	0.838421i
$910$	2.33957e10	−	4.05225e10i	0.00113096	−	0.00195889i
$911$	−2.00876e12			−0.0966262			−0.0483131	−	0.998832i	$-0.515385\pi$
$911$	−2.00876e12			−0.0966262			−0.0483131	+	0.998832i	$0.515385\pi$
$912$	−4.35666e12	−	7.54596e12i	−0.208534	−	0.361192i
$913$	6.01520e11	−	1.04186e12i	0.0286505	−	0.0496241i
$914$	−2.08212e12			−0.0986841
$915$	−6.28018e12			−0.296194
$916$	6.02797e12	−	1.04407e13i	0.282905	−	0.490007i
$917$	8.81185e12			0.411533
$918$	5.74867e12	+	9.95699e12i	0.267162	+	0.462739i
$919$	−3.10177e13			−1.43447			−0.717233	−	0.696834i	$-0.754592\pi$
$919$	−3.10177e13			−1.43447			−0.717233	+	0.696834i	$0.754592\pi$
$920$	−1.25203e13	−	2.16857e13i	−0.576193	−	0.997996i
$921$	2.60230e12	+	4.50731e12i	0.119176	+	0.206419i
$922$	−6.51173e12	−	1.12786e13i	−0.296761	−	0.514006i
$923$	−5.09853e11	+	8.83092e11i	−0.0231227	+	0.0400496i
$924$	−3.59411e12			−0.162206
$925$	2.64585e12	−	9.53466e11i	0.118830	−	0.0428220i
$926$	1.70335e12			0.0761300
$927$	5.21759e11	−	9.03713e11i	0.0232066	−	0.0401950i
$928$	2.11916e12	+	3.67050e12i	0.0937991	+	0.162465i
$929$	1.16170e12	+	2.01212e12i	0.0511708	+	0.0886304i	0.890476	−	0.455030i	$-0.150371\pi$
$929$	1.16170e12	+	2.01212e12i	0.0511708	+	0.0886304i	−0.839305	+	0.543660i	$0.817038\pi$
$930$	2.56850e11	+	4.44877e11i	0.0112592	+	0.0195014i
$931$	2.09831e13			0.915368
$932$	−1.90550e13	−	3.30042e13i	−0.827251	−	1.43284i
$933$	−1.26890e13			−0.548228
$934$	5.52563e11	−	9.57066e11i	0.0237586	−	0.0411511i
$935$	6.03677e13			2.58317
$936$	2.75330e11			0.0117250
$937$	−6.43249e12	+	1.11414e13i	−0.272616	+	0.472185i	−0.969531	−	0.244969i	$-0.921222\pi$
$937$	−6.43249e12	+	1.11414e13i	−0.272616	+	0.472185i	0.696915	+	0.717154i	$0.254555\pi$
$938$	−1.38463e12	−	2.39825e12i	−0.0584010	−	0.101154i
$939$	3.77721e12			0.158554
$940$	−2.22982e13	+	3.86217e13i	−0.931526	+	1.61345i
$941$	−6.48619e12	+	1.12344e13i	−0.269672	+	0.467086i	−0.968777	−	0.247933i	$-0.920249\pi$
$941$	−6.48619e12	+	1.12344e13i	−0.269672	+	0.467086i	0.699105	+	0.715019i	$0.253582\pi$
$942$	5.95364e11	−	1.03120e12i	0.0246351	−	0.0426692i
$943$	1.79767e13	+	3.11366e13i	0.740301	+	1.28224i
$944$	1.37053e13	+	2.37383e13i	0.561714	+	0.972918i
$945$	2.87319e12	−	4.97651e12i	0.117198	−	0.202993i
$946$	6.62759e12	−	1.14793e13i	0.269058	−	0.466022i
$947$	1.51669e13	−	2.62698e13i	0.612804	−	1.06141i	−0.377962	−	0.925821i	$-0.623375\pi$
$947$	1.51669e13	−	2.62698e13i	0.612804	−	1.06141i	0.990766	−	0.135586i	$-0.0432917\pi$
$948$	−7.14089e11			−0.0287154
$949$	−7.08089e10	−	1.22645e11i	−0.00283394	−	0.00490852i
$950$	−4.61744e11	+	7.99764e11i	−0.0183927	+	0.0318570i
$951$	1.39129e13			0.551578
$952$	−6.03643e12			−0.238185
$953$	1.54857e13	−	2.68220e13i	0.608152	−	1.05335i	−0.383393	−	0.923585i	$-0.625244\pi$
$953$	1.54857e13	−	2.68220e13i	0.608152	−	1.05335i	0.991545	−	0.129765i	$-0.0414223\pi$
$954$	5.96763e12			0.233257
$955$	1.59521e13	+	2.76298e13i	0.620586	+	1.07489i
$956$	−1.02298e13			−0.396102
$957$	2.39715e12	+	4.15198e12i	0.0923828	+	0.160012i
$958$	2.49509e12	+	4.32162e12i	0.0957064	+	0.165768i
$959$	−1.87384e12	−	3.24558e12i	−0.0715399	−	0.123911i
$960$	−4.05822e12	+	7.02905e12i	−0.154211	+	0.267101i
$961$	−2.60613e13			−0.985690
$962$	−1.90462e11	−	1.60854e11i	−0.00717001	−	0.00605543i
$963$	−4.43019e11			−0.0165999
$964$	−8.69765e12	+	1.50648e13i	−0.324381	+	0.561844i
$965$	7.54770e12	+	1.30730e13i	0.280183	+	0.485291i
$966$	1.02756e12	+	1.77978e12i	0.0379672	+	0.0657611i
$967$	−6.99779e12	−	1.21205e13i	−0.257360	−	0.445761i	0.708174	−	0.706038i	$-0.249519\pi$
$967$	−6.99779e12	−	1.21205e13i	−0.257360	−	0.445761i	−0.965534	+	0.260277i	$0.916186\pi$
$968$	1.23840e13			0.453336
$969$	−1.41751e13	−	2.45519e13i	−0.516497	−	0.894599i
$970$	6.29263e12			0.228223
$971$	2.25695e13	−	3.90916e13i	0.814772	−	1.41123i	−0.0947193	−	0.995504i	$-0.530195\pi$
$971$	2.25695e13	−	3.90916e13i	0.814772	−	1.41123i	0.909491	−	0.415723i	$-0.136471\pi$
$972$	2.58314e13			0.928216
$973$	−5.25607e12			−0.187998
$974$	1.57082e12	−	2.72075e12i	0.0559258	−	0.0968663i
$975$	−3.25812e10	−	5.64322e10i	−0.00115464	−	0.00199989i
$976$	9.89451e12			0.349036
$977$	−4.65552e12	+	8.06359e12i	−0.163472	+	0.283141i	−0.936111	−	0.351703i	$-0.885603\pi$
$977$	−4.65552e12	+	8.06359e12i	−0.163472	+	0.283141i	0.772640	+	0.634845i	$0.218936\pi$
$978$	1.98441e12	−	3.43710e12i	0.0693595	−	0.120134i
$979$	1.01913e13	−	1.76518e13i	0.354574	−	0.614140i
$980$	−1.32087e13	−	2.28781e13i	−0.457448	−	0.792323i
$981$	1.10560e13	+	1.91496e13i	0.381143	+	0.660160i
$982$	2.10089e12	−	3.63885e12i	0.0720944	−	0.124871i
$983$	−2.65889e13	+	4.60532e13i	−0.908257	+	1.57315i	−0.0917725	+	0.995780i	$0.529253\pi$
$983$	−2.65889e13	+	4.60532e13i	−0.908257	+	1.57315i	−0.816485	+	0.577367i	$0.804080\pi$
$984$	−3.91054e12	+	6.77325e12i	−0.132972	+	0.230314i
$985$	4.91309e11			0.0166300
$986$	1.91703e12	+	3.32039e12i	0.0645926	+	0.111878i
$987$	3.84342e12	−	6.65700e12i	0.128911	−	0.223281i
$988$	−8.17199e11			−0.0272848
$989$	7.56631e13			2.51479
$990$	−4.23399e12	+	7.33349e12i	−0.140085	+	0.242635i
$991$	2.84098e13			0.935699			0.467850	−	0.883808i	$-0.345029\pi$
$991$	2.84098e13			0.935699			0.467850	+	0.883808i	$0.345029\pi$
$992$	−1.45549e12	−	2.52098e12i	−0.0477207	−	0.0826546i
$993$	7.30625e12			0.238464
$994$	1.56800e12	+	2.71586e12i	0.0509458	+	0.0882408i
$995$	1.43299e12	+	2.48201e12i	0.0463489	+	0.0802786i
$996$	3.55648e11	+	6.16000e11i	0.0114513	+	0.0198342i
$997$	−2.22188e13	+	3.84840e13i	−0.712183	+	1.23354i	0.251853	+	0.967765i	$0.418960\pi$
$997$	−2.22188e13	+	3.84840e13i	−0.712183	+	1.23354i	−0.964036	+	0.265771i	$0.914373\pi$
$998$	1.96175e12			0.0625973
$999$	−2.33903e13	−	1.97543e13i	−0.743005	−	0.627504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.c.a.10.15	✓	54
37.26	even	3	inner	37.10.c.a.26.15	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.c.a.10.15	✓	54	1.1	even	1	trivial
37.10.c.a.26.15	yes	54	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.41387 - 5.91300i) q^{2} +(41.2346 + 71.4204i) q^{3} +(232.691 + 403.033i) q^{4} +(-741.590 - 1284.47i) q^{5} +563.079 q^{6} +(721.322 + 1249.37i) q^{7} +6673.32 q^{8} +(6440.92 - 11156.0i) q^{9} +O(q^{10})\)	\(q+(3.41387 - 5.91300i) q^{2} +(41.2346 + 71.4204i) q^{3} +(232.691 + 403.033i) q^{4} +(-741.590 - 1284.47i) q^{5} +563.079 q^{6} +(721.322 + 1249.37i) q^{7} +6673.32 q^{8} +(6440.92 - 11156.0i) q^{9} -10126.8 q^{10} +64912.9 q^{11} +(-19189.8 + 33237.8i) q^{12} +(1601.42 + 2773.74i) q^{13} +9850.01 q^{14} +(61158.4 - 105929. i) q^{15} +(-96355.9 + 166893. i) q^{16} +(-313509. + 543013. i) q^{17} +(-43976.9 - 76170.3i) q^{18} +(274128. + 474804. i) q^{19} +(345123. - 597770. i) q^{20} +(-59486.8 + 103034. i) q^{21} +(221605. - 383830. i) q^{22} +2.52992e6 q^{23} +(275171. + 476611. i) q^{24} +(-123350. + 213649. i) q^{25} +21868.1 q^{26} +2.68560e6 q^{27} +(-335690. + 581432. i) q^{28} +895575. q^{29} +(-417574. - 723259. i) q^{30} -615101. q^{31} +(2.36626e6 + 4.09849e6i) q^{32} +(2.67666e6 + 4.63611e6i) q^{33} +(2.14056e6 + 3.70755e6i) q^{34} +(1.06985e6 - 1.85304e6i) q^{35} +5.99497e6 q^{36} +(-8.70955e6 - 7.35564e6i) q^{37} +3.74335e6 q^{38} +(-132068. + 228748. i) q^{39} +(-4.94887e6 - 8.57169e6i) q^{40} +(7.10564e6 + 1.23073e7i) q^{41} +(406161. + 703492. i) q^{42} +2.99073e7 q^{43} +(1.51047e7 + 2.61620e7i) q^{44} -1.91061e7 q^{45} +(8.63684e6 - 1.49594e7i) q^{46} -6.46096e7 q^{47} -1.58928e7 q^{48} +(1.91362e7 - 3.31449e7i) q^{49} +(842204. + 1.45874e6i) q^{50} -5.17096e7 q^{51} +(-745271. + 1.29085e6i) q^{52} +(-3.39248e7 + 5.87594e7i) q^{53} +(9.16828e6 - 1.58799e7i) q^{54} +(-4.81388e7 - 8.33789e7i) q^{55} +(4.81361e6 + 8.33741e6i) q^{56} +(-2.26071e7 + 3.91567e7i) q^{57} +(3.05738e6 - 5.29554e6i) q^{58} +(7.11183e7 - 1.23180e8i) q^{59} +5.69240e7 q^{60} +(-2.56718e7 - 4.44648e7i) q^{61} +(-2.09988e6 + 3.63709e6i) q^{62} +1.85839e7 q^{63} -6.63560e7 q^{64} +(2.37519e6 - 4.11395e6i) q^{65} +3.65511e7 q^{66} +(-1.40571e8 - 2.43477e8i) q^{67} -2.91803e8 q^{68} +(1.04320e8 + 1.80688e8i) q^{69} +(-7.30467e6 - 1.26521e7i) q^{70} +(1.59188e8 + 2.75722e8i) q^{71} +(4.29823e7 - 7.44475e7i) q^{72} -4.42164e7 q^{73} +(-7.32272e7 + 2.63884e7i) q^{74} -2.03452e7 q^{75} +(-1.27574e8 + 2.20965e8i) q^{76} +(4.68231e7 + 8.11000e7i) q^{77} +(901724. + 1.56183e6i) q^{78} +(9.30295e6 + 1.61132e7i) q^{79} +2.85826e8 q^{80} +(-1.60371e7 - 2.77770e7i) q^{81} +9.70310e7 q^{82} +(9.26657e6 - 1.60502e7i) q^{83} -5.53682e7 q^{84} +9.29980e8 q^{85} +(1.02100e8 - 1.76842e8i) q^{86} +(3.69287e7 + 6.39623e7i) q^{87} +4.33185e8 q^{88} +(1.56999e8 - 2.71930e8i) q^{89} +(-6.52257e7 + 1.12974e8i) q^{90} +(-2.31027e6 + 4.00151e6i) q^{91} +(5.88690e8 + 1.01964e9i) q^{92} +(-2.53634e7 - 4.39308e7i) q^{93} +(-2.20569e8 + 3.82037e8i) q^{94} +(4.06582e8 - 7.04220e8i) q^{95} +(-1.95144e8 + 3.37999e8i) q^{96} -6.21385e8 q^{97} +(-1.30657e8 - 2.26305e8i) q^{98} +(4.18099e8 - 7.24168e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9 - 82404 * q^10 - 108196 * q^11 + 45492 * q^12 - 29827 * q^13 - 504992 * q^14 + 87135 * q^15 - 1561814 * q^16 + 116991 * q^17 + 1767678 * q^18 - 599677 * q^19 + 4122556 * q^20 - 221017 * q^21 - 257914 * q^22 + 1752736 * q^23 + 1149408 * q^24 - 6037260 * q^25 - 16731604 * q^26 - 1916582 * q^27 + 1917318 * q^28 - 11336100 * q^29 - 20390006 * q^30 + 14447580 * q^31 - 873740 * q^32 - 4494200 * q^33 + 13736524 * q^34 - 8546699 * q^35 + 61692836 * q^36 - 1919410 * q^37 - 85447920 * q^38 - 14035313 * q^39 + 3210182 * q^40 + 28676571 * q^41 - 101904850 * q^42 + 56602028 * q^43 + 153011074 * q^44 + 104234980 * q^45 + 99535572 * q^46 - 147509100 * q^47 - 203670880 * q^48 - 201857540 * q^49 - 91421384 * q^50 + 328228338 * q^51 - 69374156 * q^52 + 59137361 * q^53 + 201615042 * q^54 - 219079762 * q^55 + 202573590 * q^56 - 5989161 * q^57 - 157098688 * q^58 + 137993791 * q^59 + 413427232 * q^60 - 244884419 * q^61 + 109345558 * q^62 - 995908592 * q^63 + 184008092 * q^64 + 248745395 * q^65 + 1965122248 * q^66 - 130143913 * q^67 + 667610796 * q^68 + 246927272 * q^69 - 291173360 * q^70 + 473387559 * q^71 + 366188748 * q^72 + 923638972 * q^73 - 885443390 * q^74 - 2185997392 * q^75 - 337459826 * q^76 - 586609928 * q^77 - 261025842 * q^78 + 563110723 * q^79 - 4210381784 * q^80 + 713813329 * q^81 + 3458576264 * q^82 - 663594441 * q^83 - 2635249016 * q^84 - 1417287750 * q^85 - 2269028474 * q^86 + 314944482 * q^87 - 7714172 * q^88 + 655027619 * q^89 + 588021376 * q^90 - 1833870961 * q^91 - 2384055268 * q^92 - 90092600 * q^93 - 1449940302 * q^94 + 2787158841 * q^95 + 2383567424 * q^96 - 2751583248 * q^97 + 4970876154 * q^98 + 2668760954 * q^99

Introduction

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